Existence Study Of Solutions To Boundary Value Problems Of Several Classes Of Fractional Differential Equations

In recent years,there are many researches on the boundary value problem of fractional order differential equations.For example,singular problem and multi-point boundary val-ue problem with p-Laplace operator,integral boundary value problem and coupled system boundary value problem with Hadamard fractional derivative,fractional differential equa-tions boundary value problem with Riesz-Caputo derivative.With the modern progress of science and technology and the advancement of fractional order theory,fractional order dif-ferential equations have been widely used in signal and image processing,electromagnetism,mechanics,optics and other science and engineering fields.It is of profound significance for solving practical problems.In this paper,we mainly study the existence of solutions for several classes of boundary value problems of nonlinear fractional differential equations and acqure some new results.This paper consists of the following four chapters:The first chapter is the introduction and gives the definitions and lemmas related to fractional differential equations.In the second chapter,we investigate the system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions(?) By applying Krasnosel'skii's fixed point theorem,we obtain the existence of positive solutions for the boundary value problem.The third chapter is to study a class of integral boundary value problem of fractional differential equations with Riesz-Caputo derivative:(?) The existence of solutions are obtained by employing Banach fixed point theorem,Leray-Schauder alternative theory and Krasnosel'skii's fixed point theorem.In the fourth chapter,we study a class of nonlinear fractional differential equations with multi-point boundary value conditions(?)By using Leggett-Williams theorem and Krasnosel'skii's theorem,the existence of the posi-tive solution is obtained.