Study on a new [formula omitted]-Laplacian fractional differential model generated by instantaneous and non-instantaneous impulsive effects

Abstract

In this paper, we discuss a new p-Laplacian fractional differential equation involving instantaneous and non-instantaneous impulses, supplemented with Sturm–Liouville boundary conditions. To study the stated problem, we introduce a new norm for fractional space, denoted by Eα,p. Under this framework, using the critical point theorem proposed by Bonanno and Marano, we prove the existence result of multiple solutions. Finally, an illustrative example is presented.