Calculus of variations with fractional derivatives and fractional integrals

TL;DR

This paper develops Euler-Lagrange equations and optimality conditions for calculus of variations problems involving fractional derivatives and integrals, expanding classical variational calculus into the fractional domain.

Contribution

It introduces new fractional Euler-Lagrange equations and sufficiency conditions for problems with Riemann-Liouville fractional derivatives and integrals.

Findings

Derived fractional Euler-Lagrange equations.

Established sufficient optimality conditions.

Extended classical calculus of variations to fractional calculus.

Abstract

We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.