A survey on fractional variational calculus

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 Grünwald--Letnikov approximations of Caputo derivatives.

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

References in corpus (4)

• Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
• The Variable-Order Fractional Calculus of Variations
• Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems
• Existence of Minimizers for Fractional Variational Problems Containing Caputo Derivatives

Cited by in corpus (2)

• A numerical approach for solving fractional optimal control problems using modified hat functions
• The Duality Theory of Fractional Calculus and a New Fractional Calculus of Variations Involving Left Operators Only