Generalized Euler-Lagrange equations for fractional variational problems with free boundary conditions

Authors:
S. A. Yousefi;Mehdi Dehghan;A. Lotfi
Affiliations:
Department of Mathematics, Shahid Beheshti University, G. C. Tehran, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran;Department of Mathematics, Shahid Beheshti University, G. C. Tehran, Iran
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 3
Cited 1

Generalized Variational Problems and Euler-Lagrange equations

Computers & Mathematics with Applications
Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative

Computers & Mathematics with Applications
The use of He's variational iteration method for solving variational problems

International Journal of Computer Mathematics

A numerical technique for solving a class of fractional variational problems

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.10

Visualization

Abstract

In this article we are going to present necessary conditions which must be satisfied to make the fractional variational problems (FVPs) with completely free boundary conditions have an extremum. The fractional derivatives are defined in the Caputo sense. First we present the necessary conditions for the problem with only one dependent variable, and then we generalize them to problems with multiple dependent variables. We also find the transversality conditions for when each end point lies on a given arbitrary curve in the case of a single variable or a surface in the case of multiple variables. It is also shown that in special cases such as those with specified and unspecified boundary conditions and problems with integer order derivatives, the new results reduce to the known necessary conditions. Some examples are presented to demonstrate the applicability of the new formulations.