The generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative

TL;DR

This paper derives necessary and sufficient optimality conditions for fractional variational problems involving Caputo derivatives, especially when the Lagrangian depends on free end-points, advancing the theoretical framework of fractional calculus of variations.

Contribution

It introduces generalized natural boundary conditions for fractional variational problems with Caputo derivatives, extending existing theories to include free end-point dependencies.

Findings

Derived necessary and sufficient optimality conditions.

Established generalized natural boundary conditions.

Extended fractional calculus of variations theory.

Abstract

This paper presents necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrangian depending on the free end-points. The fractional derivatives are defined in the sense of Caputo.