The Euler-Lagrange and Legendre equations for functionals involving distributed-order fractional derivatives

被引：12
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, Pole CMAT UTAD, Ctr Math, Vila Real, Portugal
[3] Univ Tras Os Montes & Alto Douro, UTAD, Dept Math, Vila Real, Portugal
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 331卷
关键词：
Distributed-order fractional derivative; Euler-Lagrange equation; Legendre condition; Numerical methods; DIFFUSION EQUATION; VARIATIONAL CALCULUS; BOUNDED DOMAINS; FORMULATION;
D O I：
10.1016/j.amc.2018.03.022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we extend some fractional calculus of variations results by considering functionals depending on distributed-order fractional derivatives. Using variational techniques, we deduce optimal necessary conditions of Euler-Lagrange and Legendre type. We also study the case where integral and holonomic constraints are imposed. Finally, a numerical procedure is given to solve some proposed problems. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：394 / 403
页数：10
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