Existence And Multiplicity Of Solutions For A Class Of Fractional Differential Equation With Impulsive Effects

In this paper,we study the existence of nontrivial solution and infinitely many solutions for a class of Fractional Differential Equations with impulsive effects by using Critical Point theory.We obtain the sufficient conditions for the existence of nontrivial solution and infinitely many solutions and give some examples to explain the feasibility and viability of our results.This paper is organized as fol-lows.Firstly,we present some related background of fractional calculus theory,and introduce the research progress of the solvability of fractional differential equa-tions and the main contents of this paper.Secondly,we present some preliminary knowledge which includes the definition and property of Riemann-Liouville Frac-tional Integral,Riemann-Liouville Fractional Derivatives and Capto~?s Fractional Derivatives for proving our main results.Then we introduce related notations and some critical point theorems.Finally,in order to construct the variational func-tional,we choose appropriate fractional derivative space as the working space.By using Fountain Theorem and the Local Linking Theorem,we obtain solvability results for a class of fractional boundary problem with impulsive effects.More-over,some examples are presented to illustrate the feasibility and effectiveness of our results.