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 dierential systems. Indeed, we will use variational methods for smooth functionals, dened on the re exive 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 dierential problem has three non-negative solutions. Finally, by presenting two examples, we will ensure the applicability of our results.

Keywords

• Three solutions,Fractional dierential equation,Impulsive eect,Variational methods,Critical point theory.

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20. Shapour Heidarkhani is an Associate Professor of Mathematics in the Department of Mathematics at Razi University, Kermanshah/Iran.