On exact solutions of a class of fractional Euler-Lagrange equations

被引：97

作者：

Baleanu, Dumitru ^{[1
]}

Trujillo, Juan J. ^{[2
]}

机构：

[1] Cankaya Univ, Fac Arts & Sci, Dept Math & Comp Sci, TR-06530 Ankara, Turkey

[2] Univ La Laguna, Dept Anal Matemat, Tenerife 38271, Spain

来源：

NONLINEAR DYNAMICS | 2008年 / 52卷 / 04期

关键词：

fractional calculus; differential equations of fractional order; fractional variational calculus;

D O I：

10.1007/s11071-007-9281-7

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles. We find a fractional Lagrangian L(x(t), where D-c(a)t(alpha) x(t)) and 0 < alpha < 1, such that the following is the corresponding Euler-Lagrange D-t(b)alpha(D-c(a)t(alpha))x(t) + b(t, x(t)) ((c)(a)D(t)(alpha)x(t)) + f(t, x(t)) = 0. (1) At last, exact solutions for some Euler-Lagrange equations are presented. In particular, we consider the following equations D-t(b)alpha(D-c(a)t(alpha))x(t) = lambda x(t) (lambda is an element of R), (2) D-t(b)alpha(D-c(a)t(alpha))x(t) + g(t) D-c(a)t(alpha) x(t) = f(t), (3) where g(t) and f (t) are suitable functions.

引用

页码：331 / 335

页数：5

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