Fractional variational problems with the Riesz-Caputo derivative

• Author(s): Almeida, R.
• Date: 2012
• Persistent ID: http://hdl.handle.net/10773/4154
• Origin: RIA - Repositório Institucional da Universidade de Aveiro
• Subject(s): Calculus of variations; Isoperimetric problem; Riesz-Caputo fractional derivative
• Document Type: Article
• Language: English

Description

In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the functional is different from the interval of the fractional derivative. Next we consider integral dynamic constraints on the problem, for several different cases. Finally, we determine optimality conditions for functionals depending not only on the admissible functions, but on time also, and we present a necessary condition for a pair function-time to be an optimal solution to the problem. © 2011 Elsevier Ltd. All rights reserved. FCT CIDMA