Analysis and numerical approximation of tempered fractional calculus of variations problems

被引：15
|
作者：
Almeida, Ricardo [1 ]
Luisa Morgado, M. [2 ,3 ]
机构：
[1] Univ Aveiro, Dept Math, Ctr Res & Dev Math & Applicat CIDMA, P-3810193 Aveiro, Portugal
[2] Univ Tras Os Montes & Alto Douro, UTAD, Inst Super Tecn, Ctr Computat & Stochast Math, P-5000801 Vila Real, Portugal
[3] Univ Tras Os Montes & Alto Douro, UTAD, Dept Math, P-5000801 Vila Real, Portugal
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 361卷
关键词：
Tempered fractional derivative; Euler-Lagrange equation; Numerical methods; EULER-LAGRANGE EQUATIONS; ORDER; FORMULATION; TERMS;
D O I：
10.1016/j.cam.2019.04.010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study variational problems where the cost functional involves the tempered Caputo fractional derivative. Several important optimization conditions are derived to find the optimal solution. Sufficient and necessary conditions are presented for different variational problems. For example, the cases of integral (isoperimetric problem) and holonomic constraints are considered, as well as problems with high order derivatives. A numerical scheme is proposed to determine approximations of the solution and it is illustrated through some examples. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码：1 / 12
页数：12
相关论文
共 50 条
  • [1] WELL-POSEDNESS AND NUMERICAL APPROXIMATION OF TEMPERED FRACTIONAL TERMINAL VALUE PROBLEMS
    Morgado, Maria Luisa
    Rebelo, Magda
    [J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2017, 20 (05) : 1239 - 1262
  • [2] Well-posedness and numerical approximation of tempered fractional terminal value problems
    Maria Luísa Morgado
    Magda Rebelo
    [J]. Fractional Calculus and Applied Analysis, 2017, 20 : 1239 - 1262
  • [3] Tempered fractional calculus
    Sabzikar, Farzad
    Meerschaert, Mark M.
    Chen, Jinghua
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 293 : 14 - 28
  • [4] On Tempered and Substantial Fractional Calculus
    Cao, Jianxiong
    Li, Changpin
    Chen, YangQuan
    [J]. 2014 IEEE/ASME 10TH INTERNATIONAL CONFERENCE ON MECHATRONIC AND EMBEDDED SYSTEMS AND APPLICATIONS (MESA 2014), 2014,
  • [5] Analysis of Tempered Fractional Calculus in Holder and Orlicz Spaces
    Salem, Hussein A. H.
    Cichon, Mieczyslaw
    [J]. SYMMETRY-BASEL, 2022, 14 (08):
  • [6] ISOPERIMETRIC PROBLEMS OF THE CALCULUS OF VARIATIONS WITH FRACTIONAL DERIVATIVES
    Ricardo Almeida
    Rui A.C.Ferreira
    Delfim F.M.Torres
    [J]. Acta Mathematica Scientia, 2012, 32 (02) : 619 - 630
  • [7] ISOPERIMETRIC PROBLEMS OF THE CALCULUS OF VARIATIONS WITH FRACTIONAL DERIVATIVES
    Almeida, Ricardo
    Ferreira, Rui A. C.
    Torres, Delfim F. M.
    [J]. ACTA MATHEMATICA SCIENTIA, 2012, 32 (02) : 619 - 630
  • [8] Numerical Approximation for Fractional Diffusion Equation Forced by a Tempered Fractional Gaussian Noise
    Xing Liu
    Weihua Deng
    [J]. Journal of Scientific Computing, 2020, 84
  • [9] Numerical Approximation for Fractional Diffusion Equation Forced by a Tempered Fractional Gaussian Noise
    Liu, Xing
    Deng, Weihua
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2020, 84 (01)
  • [10] Existence, uniqueness and numerical analysis of solutions of tempered fractional boundary value problems
    Zaky, Mahmoud A.
    [J]. APPLIED NUMERICAL MATHEMATICS, 2019, 145 : 429 - 457
12345