Combined Fractional Variational Problems of Variable Order and Some Computational Aspects
Abstract
We study two generalizations of fractional variational problems by considering higher-order derivatives and a state time delay. We prove a higher-order integration by parts formula involving a Caputo fractional derivative of variable order and we establish several necessary optimality conditions for functionals containing a combined Caputo derivative of variable fractional order. Because the endpoint is considered to be free, we also deduce associated transversality conditions. In the end, we consider functionals with a time delay and deduce corresponding optimality conditions. Some examples are given to illustrate the new results. Computational aspects are discussed using the open source software package Chebfun.
Cite
@article{arxiv.1704.06486,
title = {Combined Fractional Variational Problems of Variable Order and Some Computational Aspects},
author = {Dina Tavares and Ricardo Almeida and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1704.06486},
year = {2018}
}
Comments
This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Applied Mathematics', ISSN: 0377-0427. Submitted 15-Feb-2017; Revised 17-Apr-2017; Accepted 21-Apr-2017