Fractional Herglotz variational problems of variable order
Abstract
We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved. Two different cases are considered: the fundamental problem, with one independent variable, and the general case, with several independent variables. We end with some illustrative examples of the results of the paper.
Cite
@article{arxiv.1703.09104,
title = {Fractional Herglotz variational problems of variable order},
author = {Dina Tavares and Ricardo Almeida and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1703.09104},
year = {2017}
}
Comments
This is a preprint of a paper whose final and definite form is with 'Discrete and Continuous Dynamical Systems -- Series S' (DCDS-S), ISSN 1937-1632 (print), ISSN 1937-1179 (online), available at [https://www.aimsciences.org/journals/home.jsp?journalID=15]. Paper Submitted 30-July-2016; Revised 03-Feb-2017; Accepted 27-March-2017