On a fractional boundary value problem in a weighted space

Abstract

In this paper, we prove the existence of solutions for a boundary value problem involving both left Riemann–Liouville and right Caputo fractional derivatives in a weighted space. For this, we convert the posed problem to a sum of of a contraction and a compact operator, then we apply Krasnoselskii’s fixed point theorem to conclude the existence of a nontrivial solution. We end the paper by some numerical examples illustrating the obtained results.