A generalized fractional variational problem depending on indefinite integrals: Euler–Lagrange equation and numerical solution

Abstract

The aim of this paper is to generalize the Euler–Lagrange equation obtained by Almeida et al., where fractional variational problems for Lagrangians, depending on fractional operators and depending on indefinite integrals, were studied. The new problem that we address here is for cost functionals, where the interval of integration is not the whole domain of the admissible functions, but a proper subset of it. Furthermore, we present a numerical method, based on Jacobi polynomials for solving this problem.