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.
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页码：1 / 12
页数：12
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