Fixed Point Theorems Applied In Several Versions Of Fractional Boundary Value Problems(FBVPs)

In this thesis,topological degree theory are used in several types of fractional boundary value problems(FBVPs)involving different boundary conditions.In Chapter One,we introduce the birth of fractional-calculus and its development in recent decades.In Chapter Two,we mainly introduce two frequently applied fractional derivatives and a generalized fractional derivatives,including their definitions and properties,where frac-tional derivatives are defined upon another scale function.At the same time,useful lemmas and fixed point theorems are presented.for instance,the Banach fixed point theorem,Kransnoselskii fixed point theorem and Schauder fixed point theorem,which play an important role in proving the existence results of FBVPs.In Chapters Three and Four,we verify the existence results for a nonsingular-point and a singular-point FBVP with integral boundary condition.In Chapters Five,we discuss the application of generalized fractional calculus,We prove the existence result for the generalized F-BVPs with nonlocal condition.Finally,we make a conclusion about this thesis,and some shortcoming in this thesis will be resolved in the future.