Existence of three solutions for impulsive fractional differential systems through variational methods

Abstract

This paper is devoted to the study of the multiplicity results of existence of solutions for a class of impulsive fractional differential systems. Indeed, we will use variational methods for smooth functionals, defined on the reflexive Banach spaces in order to achieve the existence of at least three solutions for these systems. In particular, in the scalar case, we will prove that the impulsive fractional differential problem has three non-negative solutions. Finally, by presenting two examples, we will ensure the applicability of our results.