Fractional variational calculus of variable order

TL;DR

This paper explores the calculus of variations involving variable order fractional integrals and derivatives, specifically using Riemann-Liouville integrals and Caputo derivatives, to extend classical variational methods.

Contribution

It introduces a framework for the calculus of variations with variable order fractional operators, combining Riemann-Liouville integrals and Caputo derivatives.

Findings

Developed new variational principles for variable order fractional calculus.

Derived Euler-Lagrange equations for the variable order fractional case.

Extended classical calculus of variations to fractional, variable order context.

Abstract

We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.