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

页码：394 / 403

页数：10

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