A survey on fractional variational calculus
Optimization and Control
2018-11-12 v1
Abstract
Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect and direct methods. In particular, we provide necessary optimality conditions of Euler-Lagrange type for the fundamental, higher-order, and isoperimetric problems, and compute approximated solutions based on truncated Gr\"{u}nwald--Letnikov approximations of Caputo derivatives.
Cite
@article{arxiv.1806.05092,
title = {A survey on fractional variational calculus},
author = {Ricardo Almeida and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1806.05092},
year = {2018}
}
Comments
This is a preprint of a paper whose final and definite form is in 'Handbook of Fractional Calculus with Applications. Vol 1: Basic Theory', De Gruyter. Submitted 29-March-2018; accepted, after a revision, 13-June-2018