Existence of solutions for a class of boundary value problems involving Riemann Liouville derivative with respect to a function

Abstract

In this article, we study some class of fractional boundary value problem involving generalized Riemann Liouville derivative with respect to a function and the p-Laplace operator. Precisely, using variational methods combined with the mountain pass theorem, we prove that such problem has a nontrivial weak solution. Our main result significantly complement and improves some previous papers in the literature.