Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

被引：1

作者：

Cruz, Fatima ^{[1
]}

Almeida, Ricardo ^{[1
]}

Martins, Natalia ^{[1
]}

机构：

[1] Univ Aveiro, Ctr Res & Dev Math & Applicat, Dept Math, P-3810193 Aveiro, Portugal

来源：

MATHEMATICS | 2021年 / 9卷 / 14期

关键词：

fractional calculus; calculus of variations; Euler-Lagrange equations; isoperimetric problems; holonomic problems; higher-order derivatives; EULER-LAGRANGE; EQUATIONS; RESPECT;

D O I：

10.3390/math9141665

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

引用

页数：18

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