Existence of Minimizers for Fractional Variational Problems Containing Caputo Derivatives

TL;DR

This paper proves the existence of solutions for fractional variational problems involving Caputo derivatives, under certain regularity, coercivity, and convexity conditions, expanding the theoretical foundation of fractional calculus of variations.

Contribution

It establishes the existence of minimizers for fractional variational problems with Caputo derivatives, a novel result in the calculus of variations involving fractional derivatives.

Findings

Existence of solutions under regularity, coercivity, and convexity.

Applicability to problems involving Riemann-Liouville and Caputo derivatives.

Theoretical advancement in fractional calculus of variations.

Abstract

We study dynamic minimization problems of the calculus of variations with Lagrangian functionals containing Riemann-Liouville fractional integrals, classical and Caputo fractional derivatives. Under assumptions of regularity, coercivity and convexity, we prove existence of solutions.