A new approach on fractional variational problems and Euler-Lagrange equations

被引：14

作者：

Bahrami, F. ^{[1
]}

Fazli, H. ^{[1
]}

Akbarfam, A. Jodayree ^{[1
]}

机构：

[1] Univ Tabriz, Fac Math Sci, Tabriz, Iran

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2015年 / 23卷 / 1-3期

关键词：

Fractional calculus; Fractional variational problems; Variational solutions; Riemann-Liouville initial and boundary conditions; Fractional Euler-Lagrange equations; MECHANICS; DERIVATIVES; CALCULUS; FORMULATION;

D O I：

10.1016/j.cnsns.2014.10.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we generalize fractional variational problems in [a, b]. We allow for the possibility that functions in the space of solution for the optimization problem can blow up at boundary points. The appropriate fractional derivative spaces are introduced and a compact embedding theorem demonstrated. We prove the existence of minimizers for the variational problems which satisfy the Euler- Lagrange equations with Riemann- Liouville boundary conditions. Our method is based on the fractional calculus of variations. An example is given to illustrate the results. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：39 / 50

页数：12

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