Existence solutions for new p-Laplacian fractional boundary value problem with impulsive effects

Abstract

Fractional differential equations have been of great interest recently. This is because of both<br /> the intensive development of the theory of fractional calculus itself and the applications of such<br /> constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dynamics<br /> of processes in which sudden, discontinuous jumps occur. For the background, theory and applications<br /> of impulsive differential equations. There have been many approaches to study the existence of solutions of impulsive fractional differential equations, such as fixed point theory, topological degree theory, upper and lower solutions methods and monotone iterative method.<br /> In this paper, we study the existence of solutions for a new class of p-Laplacian fractional<br /> boundary value problem with impulsive effects. By using critical point theory and variational<br /> methods, we give some new criteria to guarantee that the impulsive problem have infinitely<br /> many solutions.