The Existence Of Solutions For Two Class Of Fractional Differential Equations With Boundary Value Problems

This paper mainly studies the existence of solutions for two types of fractional differential equation boundary value problems.In Chapter 2,we study the positive existence of solution of a class of fractional differential equation boundary value problems with Caputo derivatives with integral boundary value conditions.We first found the Green function of the boundary value problem,and discussed some properties of the Green function.We transformed the differential equation into an equivalent integral equation.On this basis,we used the Banach contraction mapping principle,Guo-Krasnosel'skii fixed point theorem and Leggett-Williams fixed point theorem to discuss its positive solution existence and use examples to verify our conclusions.In Chapter 3,we study a class of boundary value problems for fractional differential equations with Caputo-Hadamard derivatives,and similarly transform differential equations into equivalent integral equations.On this basis,we used the Banach contraction mapping principle,Krasnosel'skii fixed point theorem,Non-linear alternative theorem and Leray-Schauder degree homotopy invariance to explore the existence of its solution,and use examples to verify our conclusion.