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1

Calculus of variations with fractional derivatives and fractional integrals

Ricardo Almeida, Delfim F.M. Torres

Journal:

Applied Mathematics Letters

Year:

2009

Language:

english

File:

PDF, 392 KB

english, 2009

2

Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan

NdaÃ¯rou, FaÃ¯Ã§al, Area, IvÃ¡n, Nieto, Juan J., Torres, Delfim F.M.

Journal:

Chaos, Solitons & Fractals

Year:

2020

File:

PDF, 1.11 MB

2020

3

Fractional calculus of variations for a combined Caputo derivative

Agnieszka B. Malinowska, Delfim F. M. Torres

Journal:

Fractional Calculus and Applied Analysis

Year:

2011

Language:

english

File:

PDF, 219 KB

english, 2011

4

Lyapunov functions for fractional-order systems in biology: Methods and applications

Boukhouima, Adnane, Hattaf, Khalid, Lotfi, El Mehdi, Mahrouf, Marouane, Torres, Delfim F.M., Yousfi, Noura

Journal:

Chaos, Solitons & Fractals

Year:

2020

File:

PDF, 937 KB

2020

5

Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives

Ricardo Almeida, Delfim F.M. Torres

Journal:

Communications in Nonlinear Science and Numerical Simulation

Year:

2011

Language:

english

File:

PDF, 283 KB

english, 2011

6

A fractional calculus of variations for multiple integrals with application to vibrating string

Almeida, Ricardo, Malinowska, Agnieszka B., Torres, Delfim F. M.

Journal:

Journal of Mathematical Physics

Year:

2010

Language:

english

File:

PDF, 349 KB

english, 2010

7

Multiobjective fractional variational calculus in terms of a combined Caputo derivative

Agnieszka B. Malinowska, Delfim F.M. Torres

Journal:

Applied Mathematics and Computation

Year:

2012

Language:

english

File:

PDF, 240 KB

english, 2012

8

Vaccination models and optimal control strategies to dengue

Rodrigues, Helena Sofia, Monteiro, M. Teresa T., Torres, Delfim F.M.

Journal:

Mathematical Biosciences

Year:

2014

Language:

english

File:

PDF, 1.04 MB

english, 2014

9

Generalizations of Gronwall–Bihari inequalities on time scales

Ferreira, Rui A.C., Torres, Delfim F.M.

Journal:

Journal of Difference Equations and Applications

Year:

2009

Language:

english

File:

PDF, 141 KB

english, 2009

10

Existence and uniqueness of solution for a fractional Riemann–Liouville initial value problem on time scales

Benkhettou, Nadia, Hammoudi, Ahmed, Torres, Delfim F.M.

Journal:

Journal of King Saud University - Science

Year:

2015

Language:

english

File:

PDF, 416 KB

english, 2015

11

Variational calculus with conformable fractional derivatives

Lazo, Matheus J., Torres, Delfim F. M.

Journal:

IEEE/ACM Transactions on Audio, Speech, and Language Processing

Year:

2017

Language:

english

File:

PDF, 552 KB

english, 2017

12

[SpringerBriefs in Applied Sciences and Technology] The Variable-Order Fractional Calculus of Variations || Expansion Formulas for Fractional Derivatives

Almeida, Ricardo, Tavares, Dina, Torres, Delfim F. M.

Year:

2019

Language:

english

File:

PDF, 853 KB

english, 2019

13

Solutions of systems with the Caputo–Fabrizio fractional delta derivative on time scales

Mozyrska, Dorota, Torres, Delfim F.M., Wyrwas, Małgorzata

Journal:

Nonlinear Analysis Hybrid Systems

Year:

2019

Language:

english

File:

PDF, 387 KB

english, 2019

14

A new spectral method based on two classes of hat functions for solving systems of fractional differential equations and an application to respiratory syncytial virus infection

Nemati, Somayeh, Torres, Delfim F. M.

Journal:

Soft Computing - A Fusion of Foundations, Methodologies and Applications

Year:

2020

Language:

english

File:

PDF, 1.19 MB

english, 2020

15

Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann–Liouville derivatives of order (α, β)

Rami Ahmad El-Nabulsi, Delfim F. M. Torres

Journal:

Mathematical Methods in the Applied Sciences

Year:

2007

Language:

english

File:

PDF, 110 KB

english, 2007

16

Fractional conservation laws in optimal control theory

Gastão S. F. Frederico, Delfim F. M. Torres

Journal:

Nonlinear Dynamics

Year:

2008

Language:

english

File:

PDF, 316 KB

english, 2008

17

Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative

Agnieszka B. Malinowska, Delfim F.M. Torres

Journal:

Computers & Mathematics with Applications

Year:

2010

Language:

english

File:

PDF, 282 KB

english, 2010

18

Fractional variational calculus with classical and combined Caputo derivatives

Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F.M. Torres

Journal:

Nonlinear Analysis: Theory, Methods & Applications

Year:

2012

Language:

english

File:

PDF, 258 KB

english, 2012

19

Numerical approximations of fractional derivatives with applications

Pooseh, Shakoor, Almeida, Ricardo, Torres, Delfim F. M.

Journal:

Asian Journal of Control

Year:

2013

Language:

english

File:

PDF, 599 KB

english, 2013

20

Dengue in Cape Verde: Vector Control and Vaccination

RODRIGUES, HELENA SOFIA, MONTEIRO, M. TERESA T., TORRES, DELFIM F. M.

Journal:

Mathematical Population Studies

Year:

2013

Language:

english

File:

PDF, 643 KB

english, 2013

21

Introduction to the Fractional Calculus of Variations ||

Malinowska, Agnieszka B, Torres, Delfim F M

Year:

2012

Language:

english

File:

PDF, 342 KB

english, 2012

22

A conformable fractional calculus on arbitrary time scales

Benkhettou, Nadia, Hassani, Salima, Torres, Delfim F.M.

Journal:

Journal of King Saud University - Science

Year:

2015

Language:

english

File:

PDF, 468 KB

english, 2015

23

Dynamics and Optimal Control of Ebola Transmission

Rachah, Amira, Torres, Delfim F. M.

Journal:

Mathematics in Computer Science

Year:

2016

Language:

english

File:

PDF, 1015 KB

english, 2016

24

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

Agarwal, Ravi P., Baleanu, Dumitru, Nieto, Juan J., Torres, Delfim F.M., Zhou, Yong

Journal:

Journal of Computational and Applied Mathematics

Year:

2017

Language:

english

File:

PDF, 875 KB

english, 2017

25

Optimal control of a nonlocal thermistor problem with ABC fractional time derivatives

Sidi Ammi, Moulay Rchid, Torres, Delfim F.M.

Journal:

Computers & Mathematics with Applications

Year:

2019

Language:

english

File:

PDF, 312 KB

english, 2019

26

Global Stability of a Caputo Fractional SIRS Model with General Incidence Rate

Sidi Ammi, Moulay Rchid, Tahiri, Mostafa, Torres, Delfim F. M.

Journal:

Mathematics in Computer Science

Year:

2020

File:

PDF, 407 KB

2020

27

Natural boundary conditions in the calculus of variations

Agnieszka B. Malinowska, Delfim F. M. Torres

Journal:

Mathematical Methods in the Applied Sciences

Year:

2010

Language:

english

File:

PDF, 171 KB

english, 2010

28

Calculus of variations on time scales with nabla derivatives

Natália Martins, Delfim F.M. Torres

Journal:

Nonlinear Analysis: Theory, Methods & Applications

Year:

2009

Language:

english

File:

PDF, 327 KB

english, 2009

29

Leitmann’s direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales

Agnieszka B. Malinowska, Delfim F.M. Torres

Journal:

Applied Mathematics and Computation

Year:

2010

Language:

english

File:

PDF, 167 KB

english, 2010

30

Fractional Noether’s theorem in the Riesz–Caputo sense

Gastão S.F. Frederico, Delfim F.M. Torres

Journal:

Applied Mathematics and Computation

Year:

2010

Language:

english

File:

PDF, 235 KB

english, 2010

31

Leitmann’s direct method for fractional optimization problems

Ricardo Almeida, Delfim F.M. Torres

Journal:

Applied Mathematics and Computation

Year:

2010

Language:

english

File:

PDF, 187 KB

english, 2010

32

Fractional variational calculus for nondifferentiable functions

Ricardo Almeida, Delfim F.M. Torres

Journal:

Computers & Mathematics with Applications

Year:

2011

Language:

english

File:

PDF, 256 KB

english, 2011

33

Modified optimal energy and initial memory of fractional continuous-time linear systems

Dorota Mozyrska, Delfim F.M. Torres

Journal:

Signal Processing

Year:

2011

Language:

english

File:

PDF, 186 KB

english, 2011

34

A formulation of Noether's theorem for fractional problems of the calculus of variations

Gastão S.F. Frederico, Delfim F.M. Torres

Journal:

Journal of Mathematical Analysis and Applications

Year:

2007

Language:

english

File:

PDF, 152 KB

english, 2007

35

Noether's theorem on time scales

Zbigniew Bartosiewicz, Delfim F.M. Torres

Journal:

Journal of Mathematical Analysis and Applications

Year:

2008

Language:

english

File:

PDF, 125 KB

english, 2008

36

Fractional variational problems depending on indefinite integrals

Ricardo Almeida, Shakoor Pooseh, Delfim F.M. Torres

Journal:

Nonlinear Analysis: Theory, Methods & Applications

Year:

2012

Language:

english

File:

PDF, 338 KB

english, 2012

37

The DuBois–Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler–Lagrange Equation Involving Only Derivatives of Caputo

Lazo, Matheus J., Torres, Delfim F. M.

Journal:

Journal of Optimization Theory and Applications

Year:

2013

Language:

english

File:

PDF, 471 KB

english, 2013

38

Generalized fractional calculus with applications to the calculus of variations

Odzijewicz, Tatiana, Malinowska, Agnieszka B., Torres, Delfim F.M.

Journal:

Computers & Mathematics with Applications

Year:

2012

Language:

english

File:

PDF, 281 KB

english, 2012

39

Green’s theorem for generalized fractional derivatives

Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres

Journal:

Fractional Calculus and Applied Analysis

Year:

2013

Language:

english

File:

PDF, 188 KB

english, 2013

40

The Second Euler-Lagrange Equation of Variational Calculus on Time Scales

Bartosiewicz, Zbigniew, Martins, Natália, Torres, Delfim F.M.

Journal:

European Journal of Control

Year:

2011

Language:

english

File:

PDF, 121 KB

english, 2011

41

Guest Editorial

de Pinho, Maria do Rosário, Fontes, Fernando A.C.C., Torres, Delfim F.M.

Journal:

European Journal of Control

Year:

2011

Language:

english

File:

PDF, 35 KB

english, 2011

42

Approximate controllability of fractional delay dynamic inclusions with nonlocal control conditions

Debbouche, Amar, Torres, Delfim F.M.

Journal:

Applied Mathematics and Computation

Year:

2014

Language:

english

File:

PDF, 500 KB

english, 2014

43

Duality for the left and right fractional derivatives

Caputo, M. Cristina, Torres, Delfim F.M.

Journal:

Signal Processing

Year:

2015

Language:

english

File:

PDF, 321 KB

english, 2015

44

[SpringerBriefs in Applied Sciences and Technology] Advanced Methods in the Fractional Calculus of Variations ||

Malinowska, Agnieszka B., Odzijewicz, Tatiana, Torres, Delfim F.M.

Year:

2015

Language:

english

File:

PDF, 3.03 MB

english, 2015

45

Optimality conditions for fractional variational problems with dependence on a combined Caputo derivative of variable order

Tavares, Dina, Almeida, Ricardo, Torres, Delfim F.M.

Journal:

Year:

2015

Language:

english

File:

PDF, 202 KB

english, 2015

46

The Diamond Integral on Time Scales

Brito da Cruz, Artur M. C., Martins, Natália, Torres, Delfim F. M.

Journal:

Bulletin of the Malaysian Mathematical Sciences Society

Year:

2015

Language:

english

File:

PDF, 203 KB

english, 2015

47

[SpringerBriefs in Electrical and Computer Engineering] Quantum Variational Calculus ||

Malinowska, Agnieszka B., Torres, Delfim F.M.

Year:

2014

Language:

english

File:

PDF, 1.50 MB

english, 2014

48

Cost-Effectiveness Analysis of Optimal Control Measures for Tuberculosis

Rodrigues, Paula, Silva, Cristiana J., Torres, Delfim F. M.

Journal:

Bulletin of Mathematical Biology

Year:

2014

Language:

english

File:

PDF, 524 KB

english, 2014

49

Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics

Odzijewicz, Tatiana, Malinowska, Agnieszka B., Torres, Delfim F. M.

Journal:

Abstract and Applied Analysis

Year:

2012

Language:

english

File:

PDF, 196 KB

english, 2012

50

Multiobjective approach to optimal control for a tuberculosis model

Denysiuk, Roman, Silva, Cristiana J., Torres, Delfim F. M.

Journal:

Optimization Methods and Software

Year:

2015

Language:

english

File:

PDF, 1.00 MB

english, 2015