Boundary Value Problems For Nonlinear Diferential Equations Of Fractional Order

Fractional diferential equations are generalizations of classical diferential equations.In recent years, fractional diferential equations have aroused international widespread atten-tions, which are one of international hot research fields. They arise in many fields such asdifusion and transport theorya chaos and turbulencea solutions chain of polymer materi-alsa viscoelasticity and non-Newtonian fluid mechanicsa signal processinga porous mediaflowa fractional controla soft material descriptiona analysis of power law phenomenon, etc.In the paper, we mainly study some classes of common boundary value problems and impul-sive boundary value problems and use a few fixed point theorems to investigate (Caputo type)existence and uniqueness of solutions for boundary value problems of nonlinear fractionaldiferential equations. The paper is organized as follows:In chapter1, we introduce theory backgrounda research situation of at home and aboardand briefly state main problems in this paper. Meanwhile we present some important fractionalorder definitionsa basic propertiesa fixed point theorems and related lemmas.In chapter2, we discuss existence and uniqueness of solutions for Sturm-Liouville bound-ary value problems and nonlocal boundary value problems and three-point boundary valueproblems of fractional diferential equations by utilizing Krasnoselski fixed point theoremand Banach fixed point theorem, respectively.In chapter3, we research boundary value problems of nonlinear fractional impulsive dif-ferential equations. Firstly, we obtain existence of solutions for impulsive diferential equa-tions by means of Altman fixed point theorem and Leray-Schauder fixed point theorem andprove uniqueness of solutions by the contraction mapping principle once more.In chapter4, we derive existence and uniqueness of solutions of nonlocal boundaryvalue problems and anti-periodic boundary value problems including two diferent fractionalLangevin equations by making use of Leray-Schauder fixed point theorem and Banach fixedpoint theorem, respectively.In chapter5, we make a brief summary for the study in the paper.