Existence Solutions For Some Classes Of Nonlinear Impulsive Fractional Differential Equations

In this paper, we discuss the existence of solutions for some classes of nonlin-ear impulsive fractional differential equations. The existence results are obtainedby applying some standard fixed point theorems. Some illustrative examples arealso presented.This thesis is divided into 4 chapters.In Chapter 1, we firstly introduce the applied background of research, mainresults, novelties, the directions of further research work of nonlinear fractionaldifferential equations and the impulsive differential equations. And some basicconcepts of fractional calculus are also introduced.In Chapter 2, we obtain the existence results of solutions for a three-point in-tegral boundary value problem of nonlinear impulsive fractional differential equa-tions by applying the Schaefer fixed point and Leray-Schauder fixed point theo-rem. Some illustrative examples are also presentedIn Chapter 3, by using the Krasnoselskii's fixed-point theorem in a cone, weget some existence results of the positive solutions for boundary value problemof nonlinear impulsive differential equations with fractional order .In Chapter 4, we investigates the existence of solutions for the boundaryvalue problem of a singular nonlinear impulsive fractional differential equations.The existence results are obtained by applying Banach contract mapping principleand Schaefer fixed point. Some illustrative examples are also presented.