A variational approach for a problem involving a ψ-hilfer fractional operator

Abstract

Boundary value problems driven by fractional operators has drawn the attention of several researchers in the last decades due to its applicabil-ity in several areas of Science and Technology. The suitable definition of the fractional derivative and its associated spaces is a natural problem that arise on the study of this kind of problem. A manner to avoid of such problem is to consider a general definition of fractional derivative. The purpose of this manuscript is to contribute, in the mentioned sense, by presenting the ψ−fractional spaces Hα,β;ψ p ([0, T ], R). As an application we study a problem, by using the Mountain Pass Theorem, which includes an wide class of equa-tions.