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 the previous ones due to C´esar [5] and Ledesma [17].