Fractional Calculus of Variations for Double Integrals

TL;DR

This paper develops fractional calculus of variations for double integrals, deriving necessary and sufficient optimality conditions using a modified Riemann-Liouville approach, including fractional PDEs and boundary conditions.

Contribution

It introduces a new framework for fractional calculus of variations with double integrals and establishes Euler-Lagrange type conditions using a recent fractional derivative approach.

Findings

Derived a necessary optimality condition in the form of a multitime fractional PDE.

Established a sufficient condition for optimality.

Formulated fractional natural boundary conditions.

Abstract

We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann-Liouville approach. A necessary optimality condition of Euler-Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions.