Existence Of Solutions For Several Kinds Of Fractional Differential Equations With Boundary Value Problems

In recent years, with the development of science and technology, fractional calculustheory not only has important applications in such fields as fluid mechanics, rheology,viscoelasticity and image processing, etc., but also has become indispensable in suchnatural science and social science as control theory, biology, financial, etc.. Fractionalcalculus is the extension of the calculus with integer order, which is of wide practicalsignificance in mathematics model. The existence of solutions for fractional differentialequation is the main content in the qualitative theory of fractional differential equation.Therefore, the solvability of the boundary value problems for fractional differentialequations is of great theoretical significance and practical value.In this thesis, the existence of solutions for multi-point boundary value problem andimpulsive boundary value problem of fractional differential equations are studiedrespectively, which based on the theory of fractional differential equation. Some examplesare presented to illustrate the main results respectively.Firstly, we discuss the existence of solutions for multi-point boundary value problemof fractional differential equations. Using Schauder fixed point theorem, Leggett-Williamsfixed point theorem, Guo-Krasnosel'skii fixed point theorem and the properties ofcorresponding fractional Green function. Some sufficient conditions for the uniqueness ofsolution and at least one or three solutions for the boundary value problem are established.Secondly, we consider the boundary value problem of fractional integrodifferentialand the boundary value problem of fractional impulsive integrodifferential, by Banachcontraction mapping principle and Schauer fixed point theorem, we give the uniqueness ofsolution and at least one solution for boundary value problems.Finally, we study the existence of solutions for impulsive boundary value problem fornonlinear differential equations of fractional order. By Banach fixed point theorem andSchauer fixed point theorem, we obtain the uniqueness of solution and at least onesolution for implusive boundary value problems.