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Ricardo Almeida completed his Ph.D. in Mathematics in 2008 from the University of Aveiro. He earned his Bachelor's degree in Mathematics in 1999 and his Master's in Mathematics in 2001 at the University of Porto, Faculty of Sciences. Currently, he holds the position of Associated Professor at the University of Aveiro. He has authored more than 100 articles in specialized journals and collaborated with 30 colleagues in co-authoring scientific works during his professional activities. He has more than 3000 citations and an h-index of 30.
Identification

Personal identification

Full name
Ricardo Miguel Moreira de Almeida
Gender
Male

Citation names

  • Almeida, Ricardo

Author identifiers

Ciência ID
C715-FBA9-2BFF
ORCID iD
0000-0002-1305-2411
Scopus Author Id
0000000213052411

Addresses

  • Aveiro. Campus Universitário de Santiago, 3810-193, Aveiro, Aveiro, Portugal (Professional)

Websites

Knowledge fields

  • Exact Sciences - Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
English Intermediate (B1) Intermediate (B1) Intermediate (B1) Intermediate (B1) Intermediate (B1)
Portuguese (Mother tongue)
Education
Degree Classification
2008
Concluded
 Matemática (Doutoramento)
Universidade de Aveiro, Portugal
"Fundamentos para Análise não standard não linear" (THESIS/DISSERTATION)
 Aprovado
2001
Concluded
 Matemática - Fundamentos e Aplicações (Mestrado)
Universidade do Porto Faculdade de Ciências, Portugal
"Teorema do Ponto fixo de Banach: algumas generalizações e aplicações." (THESIS/DISSERTATION)
 Bom com distinção
1999
Concluded
 Matemática (Licenciatura)
Universidade do Porto Faculdade de Ciências, Portugal
 16
Affiliation

Teaching in Higher Education

Category
Host institution 		Employer
2023/12/01 - Current Associate Professor (University Teacher) Universidade de Aveiro, Portugal
2010/09/01 - 2023/11/30 Assistant Professor (University Teacher) Universidade de Aveiro, Portugal
2008/09/01 - 2010 Invited Assistant Professor (University Teacher) Universidade de Aveiro, Portugal
2004 - 2008 Invited Assistant (University Teacher) Universidade de Aveiro, Portugal
2001 - 2004 Assistant (University Teacher) Universidade Portucalense Infante Dom Henrique, Portugal
Projects

Contract

Designation Funders
2019/01/01 - 2019/12/31 Centro de Investigação e Desenvolvimento em Matemática e Aplicações
UID/MAT/04106/2019
UID/MAT/04106/2013
Universidade de Aveiro, Portugal

Universidade de Aveiro Centro de Investigação e Desenvolvimento em Matemática e Aplicações, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2011/01/01 - 2013/12/31 Projecto Estratégico - UI 4106 - 2011-2012
PEst-C/MAT/UI4106/2011
PEst-OE/MAT/UI4106/2014
Universidade de Aveiro, Portugal

Universidade de Aveiro Centro de Investigação e Desenvolvimento em Matemática e Aplicações, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
Outputs

Publications

Book
  1. Almeida, R.; Malinowska, A.B.; Odzijewicz, T.. Non-invasive control of the fractional hegselmann–krause type model. 2019.
    10.1007/978-3-319-78458-8_2
  2. Almeida, R.; Tavares, D.; Torres, D.F.M.. Preface. 2019.
  3. Almeida, Ricardo; Tavares, Dina; Torres, Delfim F. M.; Almeida, Ricardo Miguel. The variable order fractional calculus of variations. Springer. 2019.
    10.1007/978-3-319-94006-9
Book chapter
  1. Ricardo Almeida. "A Numerical Scheme for a Generalized Fractional Derivative with Variable Order". 2024.
    10.1007/978-3-031-50320-7_2
  2. Ricardo Almeida; Agnieszka B. Malinowska; Tatiana Odzijewicz. "An Extension of the Fractional Gronwall Inequality". 20-28. Springer International Publishing, 2020.
    10.1007/978-3-030-17344-9_2
  3. Almeida, R.; Tavares, D.; Torres, D.F.M.. "The calculus of variations". 21-32. 2019.
    10.1007/978-3-319-94006-9_2
  4. Almeida, R.; Tavares, D.; Torres, D.F.M.. "The fractional calculus of variations". 61-113. 2019.
    10.1007/978-3-319-94006-9_4
  5. Almeida, R.; Tavares, D.; Torres, D.F.M.. "Fractional calculus". 1-19. 2019.
    10.1007/978-3-319-94006-9_1
  6. Almeida, R.; Tavares, D.; Torres, D.F.M.. "Expansion formulas for fractional derivatives". 33-59. 2019.
    10.1007/978-3-319-94006-9_3
  7. Almeida, Ricardo; Torres, Delfim F. M.. "A survey on fractional variational calculus". De Gruyter, 2019.
    10.1515/9783110571622-014
  8. Pooseh, S.; Almeida, R.; Torres, D.F.M.. "Numerical approximations to fractional problemsof the calculus of variations and optimal control". 201-240. 2014.
  9. Almeida, R.; Malinowska, A.B.; Torres, D.F.. "Fractional Euler-Lagrange differential equations via caputo derivatives". 109-118. 2012.
Conference paper
  1. Almeida, R.; Malinowska, A.B.; Odzijewicz, T.. "Fractional Opinion Formation Models with Leadership". 2018.
    10.1109/MMAR.2018.8486016
  2. Almeida, R.. "Optimization conditions for some fractional problems". 2018.
    10.1109/CONTROLO.2018.8514258
  3. Almeida, Ricardo; Bastos, R. O. Nuno; Monteiro, M. Teresa T.. "An optimization method for the best fractional order to estimate real data analysis". 2015.
  4. Almeida, Ricardo. "Variational problems with Hadamard type fractional integrals". 2014.
    10.1109/ICFDA.2014.6967382
  5. Pooseh, S.; Almeida, R.; Torres, D.F.M.. "Free time fractional optimal control problems". 2013.
Conference poster
  1. Tavares, Dina; Almeida, Ricardo; Torres, Delfim F. M.. "An isoperimetric problem with dependence on fractional derivatives". Paper presented in Research Day 2015, 2015.
Journal article
  1. Almeida, Ricardo; Girejko, Ewa; Luis Machado; Malinowska, Agnieszka B.; Martins, Natália. "Evacuation by leader-follower model with bounded confidence and predictive mechanisms". Archives of Control Sciences (2023): http://dx.doi.org/10.24425/acs.2021.138695.
    10.24425/acs.2021.138695
  2. Ricardo Almeida. "Euler–Lagrange-Type Equations for Functionals Involving Fractional Operators and Antiderivatives". Mathematics (2023): https://doi.org/10.3390/math11143208.
    10.3390/math11143208
  3. Ricardo Almeida. "Variational Problems Involving a Generalized Fractional Derivative with Dependence on the Mittag–Leffler Function". Fractal and Fractional (2023): https://doi.org/10.3390/fractalfract7060477.
    10.3390/fractalfract7060477
  4. Natália Martins; Ricardo Almeida; Cristiana J. Silva; Moulay Rchid Sidi Ammi. "Editorial for the Special Issue of Axioms “Calculus of Variations, Optimal Control and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th Birthday”". Axioms (2023): https://doi.org/10.3390/axioms12020110.
    10.3390/axioms12020110
  5. Fátima Cruz; Ricardo Almeida; Natália Martins. "Herglotz Variational Problems Involving Distributed-Order Fractional Derivatives with Arbitrary Smooth Kernels". Fractal and Fractional (2022): https://doi.org/10.3390/fractalfract6120731.
    10.3390/fractalfract6120731
  6. Ricardo Almeida. "Minimization Problems for Functionals Depending on Generalized Proportional Fractional Derivatives". Fractal and Fractional (2022): https://doi.org/10.3390/fractalfract6070356.
    10.3390/fractalfract6070356
  7. Ricardo Almeida; Ravi P. Agarwal; Snezhana Hristova; Donal O’Regan. "Stability of Gene Regulatory Networks Modeled by Generalized Proportional Caputo Fractional Differential Equations". Entropy 24 3 (2022): 372-372. https://doi.org/10.3390/e24030372.
    10.3390/e24030372
  8. Ricardo Almeida; Ravi P. Agarwal; Snezhana Hristova; Donal O’Regan. "Quadratic Lyapunov Functions for Stability of the Generalized Proportional Fractional Differential Equations with Applications to Neural Networks". Axioms 10 4 (2021): 322-322. https://doi.org/10.3390/axioms10040322.
    10.3390/axioms10040322
  9. Ricardo Almeida; Natália Martins; Cristiana J. Silva. "Global Stability Condition for the Disease-Free Equilibrium Point of Fractional Epidemiological Models". Axioms (2021): https://doi.org/10.3390/axioms10040238.
    10.3390/axioms10040238
  10. Ravi P. Agarwal; Snezhana Hristova; Donal O’Regan; Ricardo Almeida. "Approximate Iterative Method for Initial Value Problem of Impulsive Fractional Differential Equations with Generalized Proportional Fractional Derivatives". Mathematics (2021): https://doi.org/10.3390/math9161979.
    10.3390/math9161979
  11. Fátima Cruz; Ricardo Almeida; Natália Martins. "Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels". Mathematics 9 14 (2021): 1665-1665. https://doi.org/10.3390/math9141665.
    10.3390/math9141665
  12. Gastão S. F. Frederico; J. Vanterler da C. Sousa; Ricardo Almeida. "Composition functionals in higher order calculus of variations and Noether's theorem". Applicable Analysis (2021): https://doi.org/10.1080/00036811.2021.1921159.
    10.1080/00036811.2021.1921159
  13. Ricardo Almeida; Natália Martins. "New Variational Problems with an Action Depending on Generalized Fractional Derivatives, the Free Endpoint Conditions, and a Real Parameter". Symmetry (2021): https://doi.org/10.3390/sym13040592.
    10.3390/sym13040592
  14. Ricardo Almeida; Natália Martins. "A Generalization of a Fractional Variational Problem with Dependence on the Boundaries and a Real Parameter". Fractal and Fractional 5 1 (2021): 24-24. https://doi.org/10.3390/fractalfract5010024.
    10.3390/fractalfract5010024
  15. Ricardo Almeida; Rafal Kamocki; Agnieszka B. Malinowska; Tatiana Odzijewicz. "Optimal leader-following consensus of fractional opinion formation models". Journal of Computational and Applied Mathematics 381 (2021): 112996-112996. https://doi.org/10.1016/j.cam.2020.112996.
    10.1016/j.cam.2020.112996
  16. Ricardo Almeida; Natália Martins. "Fractional variational principle of Herglotz for a new class of problems with dependence on the boundaries and a real parameter". Journal of Mathematical Physics (2020): https://doi.org/10.1063/5.0021373.
    10.1063/5.0021373
  17. Ricardo Almeida. "Functional Differential Equations Involving the ¿-Caputo Fractional Derivative". Fractal and Fractional 4 2 (2020): 29-29. https://doi.org/10.3390/fractalfract4020029.
    10.3390/fractalfract4020029
  18. Ricardo Almeida; Ewa Girejko; Snezhana Hristova; Agnieszka Malinowska. "On Leader-Following Consensus in Multi-Agent Systems with Discrete Updates at Random Times". Entropy 22 6 (2020): 650-650. https://doi.org/10.3390/e22060650.
    10.3390/e22060650
  19. Ricardo Almeida; M. Luísa Morgado. "Analysis and numerical approximation of tempered fractional calculus of variations problems". Journal of Computational and Applied Mathematics 361 (2019): 1-12. https://doi.org/10.1016/j.cam.2019.04.010.
    10.1016/j.cam.2019.04.010
  20. Ricardo Almeida; Agnieszka B. Malinowska; Tatiana Odzijewicz. "On systems of fractional differential equations with the ¿ -Caputo derivative and their applications". Mathematical Methods in the Applied Sciences (2019): https://doi.org/10.1002/mma.5678.
    10.1002/mma.5678
  21. Almeida, R.; Jleli, M.; Samet, B.. "A numerical study of fractional relaxation–oscillation equations involving ¿ -Caputo fractional derivative". Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 113 3 (2019): 1873-1891. http://www.scopus.com/inward/record.url?eid=2-s2.0-85066476689&partnerID=MN8TOARS.
    10.1007/s13398-018-0590-0
  22. Almeida, R.; Girejko, E.; Hristova, S.; Malinowska, A.B.. "Leader-following consensus for fractional multi-agent systems". Advances in Difference Equations 2019 1 (2019): http://www.scopus.com/inward/record.url?eid=2-s2.0-85069747876&partnerID=MN8TOARS.
    10.1186/s13662-019-2235-9
  23. Almeida, R.; Malinowska, A.B.; Odzijewicz, T.. "Optimal Leader–Follower Control for the Fractional Opinion Formation Model". Journal of Optimization Theory and Applications 182 3 (2019): 1171-1185. http://www.scopus.com/inward/record.url?eid=2-s2.0-85051850653&partnerID=MN8TOARS.
    10.1007/s10957-018-1363-9
  24. Ricardo Almeida; Ewa Girejko; Luís Machado; Agnieszka B. Malinowska; Natália Martins. "Application of predictive control to the Hegselmann-Krause model". Mathematical Methods in the Applied Sciences 41 18 (2018): 9191-9202. https://doi.org/10.1002/mma.5132.
    10.1002/mma.5132
  25. Ricardo Almeida; Artur M. C. Brito da Cruz; Natália Martins; M. Teresa T. Monteiro. "An epidemiological MSEIR model described by the Caputo fractional derivative". International Journal of Dynamics and Control (2018): https://doi.org/10.1007/s40435-018-0492-1.
    10.1007/s40435-018-0492-1
  26. Ricardo Almeida. "Analysis of a fractional SEIR model with treatment". Applied Mathematics Letters 84 (2018): 56-62. https://doi.org/10.1016/j.aml.2018.04.015.
    10.1016/j.aml.2018.04.015
  27. Dina Tavares; Ricardo Almeida; Delfim F.M. Torres. "Combined fractional variational problems of variable order and some computational aspects". Journal of Computational and Applied Mathematics 339 (2018): 374-388. https://doi.org/10.1016/j.cam.2017.04.042.
    10.1016/j.cam.2017.04.042
  28. Ricardo Almeida; M. Luísa Morgado. "The Euler–Lagrange and Legendre equations for functionals involving distributed–order fractional derivatives". Applied Mathematics and Computation 331 (2018): 394-403. https://doi.org/10.1016/j.amc.2018.03.022.
    10.1016/j.amc.2018.03.022
  29. Ricardo Almeida; Agnieszka B. Malinowska; M.Teresa T. Monteiro. "Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications". Mathematical Methods in the Applied Sciences (2018): https://doi.org/10.1002/mma.4617.
    10.1002/mma.4617
  30. Almeida, Ricardo. "Optimality conditions for fractional variational problems with free terminal time". Discrete and Continuous Dynamical Systems - Series S 11 1 (2018): 1-19. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85031026737&doi=10.3934%2fdcdss.2018001&partnerID=40&md5=81135e7dd5e6839397914a9afa211585.
    10.3934/dcdss.2018001
  31. Almeida, Ricardo. "Fractional Herglotz variational problems of variable order". Discrete and Continuous Dynamical Systems - Series S 11 1 (2018): 143-154. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85030998778&doi=10.3934%2fdcdss.2018009&partnerID=40&md5=b99633024a24aa5388d4c1519daa2678.
    10.3934/dcdss.2018009
  32. Torres, D.F.M.; Almeida, R.; Fortes, P.; Mozyrska, D.. "The Cape Verde International Days on Mathematics 2017". Statistics, Optimization and Information Computing 6 1 (2018): 1-3. http://www.scopus.com/inward/record.url?eid=2-s2.0-85042616969&partnerID=MN8TOARS.
    10.19139/soic.v6i1.464
  33. Almeida, R.; Bastos, N.R.O.; Monteiro, M.T.T.. "A fractional Malthusian growth model with variable order using an optimization approach". Statistics, Optimization and Information Computing 6 1 (2018): 4-11. http://www.scopus.com/inward/record.url?eid=2-s2.0-85042614062&partnerID=MN8TOARS.
    10.19139/soic.v6i1.465
  34. Fard, O.S.; Soolaki, J.; Almeida, R.. "A formulation of Noether’s theorem for fuzzy problems of the calculus of variations". Afrika Matematika 29 1-2 (2018): 33-46. http://www.scopus.com/inward/record.url?eid=2-s2.0-85044597845&partnerID=MN8TOARS.
    10.1007/s13370-017-0524-6
  35. Torres, D.F.M.; Almeida, R.; Malinowska, A.B.; Martins, N.; Sidi Ammi, M.R.. "Introduction: New trends on dynamical systems and differential equations". International Journal of Dynamical Systems and Differential Equations 8 1-2 (2018): 1-5. http://www.scopus.com/inward/record.url?eid=2-s2.0-85040440150&partnerID=MN8TOARS.
  36. Ricardo Almeida. "Fractional Differential Equations with Mixed Boundary Conditions". Bulletin of the Malaysian Mathematical Sciences Society (2017): https://doi.org/10.1007/s40840-017-0569-6.
    10.1007/s40840-017-0569-6
  37. Ricardo Almeida. "A Caputo fractional derivative of a function with respect to another function". Communications in Nonlinear Science and Numerical Simulation 44 (2017): 460-481. https://doi.org/10.1016%2Fj.cnsns.2016.09.006.
    10.1016/j.cnsns.2016.09.006
  38. Almeida, Ricardo. "Variational methods for the solution of fractional discrete/continuous Sturm-Liouville problems". Journal of Mechanics of Materials and Structures 12 1 (2017): 3-21. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85019588429&doi=10.2140%2fjomms.2017.12.3&partnerID=40&md5=64c7eda2b71ed385d25097635e1cd2c1.
    10.2140/jomms.2017.12.3
  39. Almeida, Ricardo. "A gronwall inequality for a general caputo fractional operator". Mathematical Inequalities and Applications 20 4 (2017): 1089-1105. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85031671317&doi=10.7153%2fmia-2017-20-70&partnerID=40&md5=ca3f65ee6518458db176fd603af25f92.
    10.7153/mia-2017-20-70
  40. Almeida, Ricardo. "Variational Problems Involving a Caputo-Type Fractional Derivative". Journal of Optimization Theory and Applications 174 1 (2017): 276-294. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84957637155&doi=10.1007%2fs10957-016-0883-4&partnerID=40&md5=77197485d5b7517e6e4c38439b12f058.
    10.1007/s10957-016-0883-4
  41. Almeida, Ricardo. "What is the best fractional derivative to fit data?". Applicable Analysis and Discrete Mathematics 11 2 (2017): 358-368. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85031942691&doi=10.2298%2fAADM170428002A&partnerID=40&md5=010d72aaeb2c100d09e9c60a48459ed4.
    10.2298/AADM170428002A
  42. Almeida, Ricardo. "Caputo–Hadamard Fractional Derivatives of Variable Order". Numerical Functional Analysis and Optimization 38 1 (2017): 1-19. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85008319064&doi=10.1080%2f01630563.2016.1217880&partnerID=40&md5=206b170faa462a325f44357ad758866d.
    10.1080/01630563.2016.1217880
  43. Tavares, D.; Almeida, R.; Torres, D.F.M.. "Constrained fractional variational problems of variable order". IEEE/CAA Journal of Automatica Sinica 4 1 (2017): 80-88. http://www.scopus.com/inward/record.url?eid=2-s2.0-85010032197&partnerID=MN8TOARS.
    10.1109/JAS.2017.7510331
  44. Almeida, Ricardo. "Modeling some real phenomena by fractional differential equations". Mathematical Methods in the Applied Sciences 39 16 (2016): 4846-4855. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84951728518&doi=10.1002%2fmma.3818&partnerID=40&md5=271a7a44572f8b344185fa727212221d.
    10.1002/mma.3818
  45. Almeida, Ricardo. "A remark on local fractional calculus and ordinary derivatives". Open Mathematics 14 1 (2016): 1122-1124. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85015819135&doi=10.1515%2fmath-2016-0104&partnerID=40&md5=9a99fd1440ab8dad274729ebf1e8cc0f.
    10.1515/math-2016-0104
  46. Almeida, Ricardo. "Caputo derivatives of fractional variable order: Numerical approximations". Communications in Nonlinear Science and Numerical Simulation 35 (2016): 69-87. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84951797580&doi=10.1016%2fj.cnsns.2015.10.027&partnerID=40&md5=a69d70c85736a95992f3f82c17460a6d.
    10.1016/j.cnsns.2015.10.027
  47. Almeida, Ricardo. "Fractional Variational Problems Depending on Indefinite Integrals and with Delay". Bulletin of the Malaysian Mathematical Sciences Society 39 4 (2016): 1515-1528. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84988345206&doi=10.1007%2fs40840-015-0248-4&partnerID=40&md5=2cafc8bd28f9eabb19e1155e72dd5333.
    10.1007/s40840-015-0248-4
  48. Almeida, Ricardo. "Fractional differential equations with dependence on the caputo-katugampola derivative". Journal of Computational and Nonlinear Dynamics 11 6 (2016): https://www.scopus.com/inward/record.uri?eid=2-s2.0-84989172214&doi=10.1115%2f1.4034432&partnerID=40&md5=3d019eb1a06ef9afd5c631fe85a810c4.
    10.1115/1.4034432
  49. Almeida, Ricardo. "A Numerical Method to Solve Higher-Order Fractional Differential Equations". Mediterranean Journal of Mathematics 13 3 (2016): 1339-1352. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84923876242&doi=10.1007%2fs00009-015-0550-2&partnerID=40&md5=de01e6433c4f3bc735a7cfb9b4d30ad3.
    10.1007/s00009-015-0550-2
  50. Almeida, R.. "A scale variational principle of Herglotz". Publicationes Mathematicae 89 1-2 (2016): 187-201. http://www.scopus.com/inward/record.url?eid=2-s2.0-85045340395&partnerID=MN8TOARS.
    10.5486/PMD.2016.7463
  51. BASTOS, NUNO; Almeida, Ricardo. "A Discretization of the Hadamard fractional derivative". MATHEMATICAL SCIENCES AND APPLICATIONS E-NOTES 4 1 (2016): 31-39.
    Published
  52. Almeida, Ricardo. "A discrete method to solve fractional optimal control problems". Nonlinear Dynamics 80 4 (2015): 1811-1816. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84929521417&doi=10.1007%2fs11071-014-1378-1&partnerID=40&md5=2322e7d5d4ad290579f2d5b54dd5efa1.
    10.1007/s11071-014-1378-1
  53. Almeida, Ricardo. "Computing Hadamard type operators of variable fractional order". Applied Mathematics and Computation 257 (2015): 74-88. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84925461334&doi=10.1016%2fj.amc.2014.12.071&partnerID=40&md5=b84c39d4f094c0fd58eb7ffc9b430abc.
    10.1016/j.amc.2014.12.071
  54. Almeida, Ricardo. "Numerical solution for fractional variational problems using the Jacobi polynomials". Applied Mathematical Modelling 39 21 (2015): 6461-6470. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84947486867&doi=10.1016%2fj.apm.2015.01.060&partnerID=40&md5=268f5d3111f11731c171d75b76fd8ce4.
    10.1016/j.apm.2015.01.060
  55. Almeida, Ricardo. "Optimality conditions for fractional variational problems with dependence on a combined Caputo derivative of variable order". Optimization 64 6 (2015): 1381-1391. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84926258370&doi=10.1080%2f02331934.2015.1010088&partnerID=40&md5=31dc55578a5e5193cf3f60185972a3f2.
    10.1080/02331934.2015.1010088
  56. Almeida, Ricardo. "Variational problems for Hölderian functions with free terminal point". Mathematical Methods in the Applied Sciences 38 6 (2015): 1059-1069. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84925361531&doi=10.1002%2fmma.3128&partnerID=40&md5=4610793c5ddee5286af507f2e5499cda.
    10.1002/mma.3128
  57. Almeida, Ricardo. "Existence results for fractional q-difference equations of order a¿]2, 3[ with three-point boundary conditions". Communications in Nonlinear Science and Numerical Simulation 19 6 (2014): 1675-1685. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84890794738&doi=10.1016%2fj.cnsns.2013.10.018&partnerID=40&md5=259bb648327eabf58ad2a930f1d64964.
    10.1016/j.cnsns.2013.10.018
  58. Almeida, Ricardo. "Fractional variational principle of herglotz". Discrete and Continuous Dynamical Systems - Series B 19 8 (2014): 2367-2381. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84907061128&doi=10.3934%2fdcdsb.2014.19.2367&partnerID=40&md5=75bd3784508d783b8cf7107cd5b39f51.
    10.3934/dcdsb.2014.19.2367
  59. Pooseh, S.; Almeida, R.; Torres, D.F.M.. "Fractional order optimal control problems with free terminal time". Journal of Industrial and Management Optimization 10 2 (2014): 363-381. http://www.scopus.com/inward/record.url?eid=2-s2.0-84886731385&partnerID=MN8TOARS.
    10.3934/jimo.2014.10.363
  60. BASTOS, NUNO; Almeida, Ricardo; Torres, Delfim F. M.. "A Discretization Method to Solve Fractional Variational Problems with Dependence on Hadamard Derivatives". International Journal of Difference Equations 9 1 (2014): 3-10.
    Published
  61. Almeida, R.; Torres, D.F.M.. "An expansion formula with higher-order derivatives for fractional operators of variable order". The Scientific World Journal 2013 (2013): http://www.scopus.com/inward/record.url?eid=2-s2.0-84890106338&partnerID=MN8TOARS.
    10.1155/2013/915437
  62. Pooseh, S.; Almeida, R.; Torres, D.F.M.. "Discrete direct methods in the fractional calculus of variations". Computers and Mathematics with Applications 66 5 (2013): 668-676. http://www.scopus.com/inward/record.url?eid=2-s2.0-84881477239&partnerID=MN8TOARS.
    10.1016/j.camwa.2013.01.045
  63. Almeida, R.; Khosravian-Arab, H.; Shamsi, M.. "A generalized fractional variational problem depending on indefinite integrals: Euler-Lagrange equation and numerical solution". JVC/Journal of Vibration and Control 19 14 (2013): 2177-2186. http://www.scopus.com/inward/record.url?eid=2-s2.0-84883717390&partnerID=MN8TOARS.
    10.1177/1077546312458818
  64. Pooseh, S.; Almeida, R.; Torres, D.F.M.. "A discrete time method to the first variation of fractional order variational functionals". Central European Journal of Physics (2013): 1-6. http://www.scopus.com/inward/record.url?eid=2-s2.0-84878006511&partnerID=MN8TOARS.
    10.2478/s11534-013-0250-0
  65. Almeida, R.. "General necessary conditions for infinite horizon fractional variational problems". Applied Mathematics Letters 26 7 (2013): 787-793. http://www.scopus.com/inward/record.url?eid=2-s2.0-84876695196&partnerID=MN8TOARS.
    10.1016/j.aml.2013.03.007
  66. Almeida, R.; Malinowska, A.B.. "Generalized transversality conditions in fractional calculus of variations". Communications in Nonlinear Science and Numerical Simulation 18 3 (2013): 443-452. http://www.scopus.com/inward/record.url?eid=2-s2.0-84867454439&partnerID=MN8TOARS.
    10.1016/j.cnsns.2012.07.009
  67. Pooseh, S.; Almeida, R.; Torres, D.F.M.. "Numerical approximations of fractional derivatives with applications". Asian Journal of Control 15 3 (2013): 698-712. http://www.scopus.com/inward/record.url?eid=2-s2.0-84877663185&partnerID=MN8TOARS.
    10.1002/asjc.617
  68. Almeida, R.; Pooseh, S.; Torres, D.F.M.. "Fractional variational problems depending on indefinite integrals". Nonlinear Analysis, Theory, Methods and Applications 75 3 (2012): 1009-1025. http://www.scopus.com/inward/record.url?eid=2-s2.0-82155197606&partnerID=MN8TOARS.
    10.1016/j.na.2011.02.028
  69. Almeida, R.; Ferreira, R.A.C.; Torres, D.F.M.. "Isoperimetric problems of the calculus of variations with fractional derivatives". Acta Mathematica Scientia 32 2 (2012): 619-630. http://www.scopus.com/inward/record.url?eid=2-s2.0-84857758121&partnerID=MN8TOARS.
    10.1016/S0252-9602(12)60043-5
  70. Almeida, R.. "Fractional variational problems with the RieszCaputo derivative". Applied Mathematics Letters 25 2 (2012): 142-148. http://www.scopus.com/inward/record.url?eid=2-s2.0-80053201237&partnerID=MN8TOARS.
    10.1016/j.aml.2011.08.003
  71. Pooseh, S.; Almeida, R.; Torres, D.F.M.. "Approximation of fractional integrals by means of derivatives". Computers and Mathematics with Applications 64 10 (2012): 3090-3100. http://www.scopus.com/inward/record.url?eid=2-s2.0-84867468500&partnerID=MN8TOARS.
    10.1016/j.camwa.2012.01.068
  72. Pooseh, S.; Almeida, R.; Torres, D.F.M.. "Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative". Numerical Functional Analysis and Optimization 33 3 (2012): 301-319. http://www.scopus.com/inward/record.url?eid=2-s2.0-84862296342&partnerID=MN8TOARS.
    10.1080/01630563.2011.647197
  73. Almeida, R.; Torres, D.F.M.. "Nondifferentiable variational principles in terms of a quantum operator". Mathematical Methods in the Applied Sciences 34 18 (2011): 2231-2241. http://www.scopus.com/inward/record.url?eid=2-s2.0-82455210837&partnerID=MN8TOARS.
    10.1002/mma.1523
  74. Almeida, R.; Torres, D.F.M.. "Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives". Communications in Nonlinear Science and Numerical Simulation 16 3 (2011): 1490-1500. http://www.scopus.com/inward/record.url?eid=2-s2.0-77957362548&partnerID=MN8TOARS.
    10.1016/j.cnsns.2010.07.016
  75. Almeida, R.; Torres, D.F.M.. "Fractional variational calculus for nondifferentiable functions". Computers and Mathematics with Applications 61 10 (2011): 3097-3104. http://www.scopus.com/inward/record.url?eid=2-s2.0-79955797338&partnerID=MN8TOARS.
    10.1016/j.camwa.2011.03.098
  76. Almeida, R.; Torres, D.F.M.. "Generalized Euler-Lagrange Equations for Variational Problems with Scale Derivatives". Letters in Mathematical Physics 92 3 (2010): 221-229. http://www.scopus.com/inward/record.url?eid=2-s2.0-77953021555&partnerID=MN8TOARS.
    10.1007/s11005-010-0385-5
  77. Almeida, R.; Torres, D.F.M.. "Leitmann's direct method for fractional optimization problems". Applied Mathematics and Computation 217 3 (2010): 956-962. http://www.scopus.com/inward/record.url?eid=2-s2.0-77957267794&partnerID=MN8TOARS.
    10.1016/j.amc.2010.03.085
  78. Almeida, R.; Malinowska, A.B.; Torres, D.F.M.. "A fractional calculus of variations for multiple integrals with application to vibrating string". Journal of Mathematical Physics 51 3 (2010): http://www.scopus.com/inward/record.url?eid=2-s2.0-77950867099&partnerID=MN8TOARS.
    10.1063/1.3319559
  79. Almeida, Ricardo. "Connectedness and compactness on standard sets". (2010):
    10.1002/malq.200810036
  80. Almeida, R.; Torres, D.F.M.. "Calculus of variations with fractional derivatives and fractional integrals". Applied Mathematics Letters 22 12 (2009): 1816-1820. http://www.scopus.com/inward/record.url?eid=2-s2.0-70349490327&partnerID=MN8TOARS.
    10.1016/j.aml.2009.07.002
  81. Almeida, R.; Neves, V.; Plakhov, A.. "Retroreflecting curves in nonstandard analysis". Journal of Mathematical Physics, Analysis, Geometry 5 1 (2009): 12-24. http://www.scopus.com/inward/record.url?eid=2-s2.0-84883818744&partnerID=MN8TOARS.
  82. Almeida, R.; Torres, D.F.M.. "Relaxed optimality conditions for mu-differentiable functions". International Journal of Applied Mathematics and Statistics 14 M09 (2009): 53-66. http://www.scopus.com/inward/record.url?eid=2-s2.0-70149093133&partnerID=MN8TOARS.
  83. Almeida, R.; Torres, D.F.M.. "Hölderian variational problems subject to integral constraints". Journal of Mathematical Analysis and Applications 359 2 (2009): 674-681. http://www.scopus.com/inward/record.url?eid=2-s2.0-67650544428&partnerID=MN8TOARS.
    10.1016/j.jmaa.2009.06.029
  84. Almeida, R.; Torres, D.F.M.. "Isoperimetric problems on time scales with nabla derivatives". JVC/Journal of Vibration and Control 15 6 (2009): 951-958. http://www.scopus.com/inward/record.url?eid=2-s2.0-66249145058&partnerID=MN8TOARS.
    10.1177/1077546309103268
  85. Almeida, R.; Neves, V.. "A strong form of almost differentiability". Journal of Mathematical Sciences 161 6 (2009): 894-908. http://www.scopus.com/inward/record.url?eid=2-s2.0-70350344025&partnerID=MN8TOARS.
    10.1007/s10958-009-9609-6
  86. Almeida, Ricardo; Torres, Delfim F. M.. "A mu-differentiable Lagrange multiplier rule". Int. J. Math. Stat. 4 S09 (2009): 57-62. http://arxiv.org/abs/0806.3553.
    Published
  87. Almeida, R.. "An elementary proof of a converse mean-value theorem". International Journal of Mathematical Education in Science and Technology 39 8 (2008): 1110-1111. http://www.scopus.com/inward/record.url?eid=2-s2.0-54049139572&partnerID=MN8TOARS.
    10.1080/00207390802276218
  88. Almeida, R.. "On the continuity of functions". Applied Sciences 9 (2007): 1-4. http://www.scopus.com/inward/record.url?eid=2-s2.0-38549091094&partnerID=MN8TOARS.
  89. Almeida, R.. "A nonstandard characterization of regular surfaces". Balkan Journal of Geometry and its Applications 12 2 (2007): 1-7. http://www.scopus.com/inward/record.url?eid=2-s2.0-34548316409&partnerID=MN8TOARS.
Journal issue
  1. Martins, Natália; Almeida, Ricardo; Silva, Cristiana J.. "Special Issue: "Calculus of Variations, Optimal Control, and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th Birthday"". Axioms (2022): https://www.mdpi.com/journal/axioms/special_issues/delfim.
Newspaper article
  1. Almeida, Ricardo; Bastos, Nuno R.O.. "An approximation formula for the Katugampola integral", The objective of this paper is to present an approximation formula for the Katugampola fractional integral, that allows us to solve fractional problems with dependence on this type of fractional operator. The formula only depends on first-order derivatives, and thus converts the fractional problem into a standard one. With some examples, we show the accuracy of the method, and then we present the , 2016, http://hdl.handle.net/10773/15021.
Thesis / Dissertation
  1. Tavares, Dina dos Santos. "Fractional calculus of variations". PhD, 2017. http://hdl.handle.net/10773/22184.
  2. Paião, Ana Pedro Lemos. "Introduction to optimal control theory and its application to diabetes". Master, 2015. http://hdl.handle.net/10773/16806.
  3. Pooseh, Shakoor. "Computational methods in the fractional calculus of variations and optimal control". PhD, 2013. http://hdl.handle.net/10773/11510.
  4. Almeida, Ricardo Miguel Moreira de. "Foundations of nonstandard non-linear analysis". PhD, 2008. http://hdl.handle.net/10773/2937.
  5. Almeida, Ricardo Miguel Moreira de. "Teorema do Ponto Fixo de Banach : Algumas generalizações e aplicações". Master, 2001. http://hdl.handle.net/10216/9558.
Activities

Oral presentation

Presentation title Event name
Host (Event location)
2023 Necessary conditions to optimize functionals involving a generalized fractional derivative
2023 A numerical scheme for a generalized fractional derivative with variable order
2022 Optimization conditions for functionals dealing with variable order fractional derivatives and with dependence on an arbitrary function
2022 Variational problems of variable fractional order involving arbitrary kernels
2022 Calculus of variation problems for variable order general fractional calculus
2021 Optimization conditions for a generalization of the tempered fractional derivative
2021 Some generalizations of the Herglotz problem involving the Mittag--Leffler tempered fractional derivative
2020 Some calculus of variations problems dealing with the distributed-order fractional derivative
2019 Variational problems involving distributed-order fractional derivatives IMAME2019, The International Meeting on Applied Mathematics and Evolution
(La Rochelle, France)
2019 Optimality conditions for functionals involving distributed-order fractional derivatives ICDEA2019, The 25th International Conference on Difference Equations and Applications
(Londres, United Kingdom)
2019 Calculus of variations with distributed-order fractional derivatives: analytical and numerical solutions SciCADE, The International Conference on Scientific Computation and Differential Equations
(Innsbruck, Austria)
2019 Fractional Euler--Lagrange equations: analytical and numerical tools The 7th International Conference on Control, Mechatronics and Automation
(Delft, Netherlands)
2019 Fractional differential equations: existence results and some applications 8th Podlasie Conference on Mathematics
(Bialystok, Poland)
2018 Optimization conditions for fractional variational problems of variable order Controlo 2018
(Ponta Delgada, Portugal)
2018 Euler--Lagrange equations for fractional variational problems SIMAI 2018, Italian Society of Applied and Industrial Mathematics
(Roma, Italy)
2018 Fractional differential equations with some applications The XII-th International Conference of Differential Geometry and Dynamical Systems
(Mangália, Romania)
2017 Fractional optimality conditions of calculus of variations The Cape Verde International Days on Mathematics 2017
(Praia, Cape Verde)
2017 Variational Problems Involving a Caputo-Type Fractional Derivative International Conference on Elliptic and Parabolic Problems
(Gaeta, Italy)
2017 Fractional differential equations: Existence and uniqueness of solutions, with applications International Conference on Mathematical Modelling in Applied Sciences
(Sâo Petersburgo, Russia)
2017 Fractional differential equations: Existence and uniqueness of solutions, with applications Workshop on Coding, Systems and Control
(Aveiro, Portugal)
2016 Modelling some phenomena by fractional differential equations International Meeting on Applied Mathematics in Errachidia
(Errachidia, Morocco)
2016 The population growth modeled by a FDE 7th Podlasie Conference on Mathematics
(Bialystok, Poland)
2016 Data fitting with respect to fractional derivatives Dynamical Systems and Applications IV
(Lodz, Poland)
2016 Natural models described by fractional derivatives Barcelona Analysis Conference 2016
(Barcelona, Spain)
2015 Variational problems with dependence on the Caputo--Katugampola derivative The Cape Verde International Days on Mathematics 2015
(S. Vincente, Cape Verde)
2015 The Caputo--Katugampola fractional derivative: properties and optimization problems AMS--EMS--SPM International Meeting 2015
(Porto, Portugal)
2015 On a Caputo type fractional operator 4th International Eurasian Conference on Mathematical Sciences and Applications
(Atenas, Greece)
2014 A numerical scheme for fractional operators of variable order EURO Mini-conference on Optimization in the Natural Sciences
(Aveiro, Portugal)
2014 Approximation formulas for fractional derivatives of variable order The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
(Madrid, Spain)
2013 Fractional order optimal control: analytical and numerical solutions EPCO 2013-- Portuguese Meeting on Optimal Control
(Porto, Portugal)
2013 Fractional Optimal Control Problems with Free Terminal Time The Cape Verde International Days on Mathematics 2013
(Praia, Cape Verde)
2013 On a discrete direct method to solve fractional variational problems PODE -- Progress on Difference Equations
(Bialystok, Poland)
2012 A numerical method to solve fractional variational problems 5th Podlasie Conference on Mathematics
(Bialystok, Poland)
2012 A new expansion formula for the Hadamard fractional integral and fractional derivative International conference on differential equations, difference equations and special functions
(Patras, Greece)
2011 Variational calculus with a discrete derivative PODE 2011 Progress on Difference Equations
(Dublin, Ireland)
2010 Euler-Lagrange equations for the Caputo fractional derivative 3rd Conference on Nonlinear Science and Complexity
(Ancara, Turkey)
2009 Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives Workshop in Control, Nonsmooth Analysis and Optimization
(Porto, Portugal)
2006 Mu-differentiability of an internal function NonStandard Methods and Applications in Mathematics
(Pisa, Italy)

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2018/09/01 - 2019/11/30 Uma abordagem ao Cálculo das Variações e Teoria do Controlo Ótimo
Supervisor
2018/09/01 - 2019/07/15 Condições necessárias e suficientes de otimalidade para funcionais dependendo de derivadas fracionárias de ordem variável
Supervisor
2014/01/01 - 2017/01/02 Fractional Calculus of Variations
Supervisor
2015 - 2015 Introdução à teoria do controlo ótimo e sua aplicação à diabetes
Supervisor
 Matemática e Aplicações (Master)
Universidade de Aveiro, Portugal
2009/01/09 - 2013/02/13 Computational Methods in the Calculus of Variations and Optimal Control
Co-supervisor
 Mathematics (PhD)
Universidade de Aveiro, Portugal
2008 - 2008 Cálculo das variações fracionário
Supervisor
 Matemática e Aplicações (PhD)
Universidade de Aveiro, Portugal
Distinctions

Award

2023 Axioms - 2023 Best Paper Award, for the publication
2012 Prémio jovem doutor CIDMA