Existence Of Solutions For Boundary Value Problems Of Some Nonlinear Q-Difference Equations

In this paper,we are concerned with the existence of solutions for three types of fractional differential equation,involving semipositone boundary value problem,integral boundary value problem of Caputo type and three points boundary value problem with p-Laplacian operator.The existence,uniqueness of solution or positive solution are studied and obtained.The theses is divided into four chapters altogether.The first chapter is introduction the history and evolution have been introduced,the relevant definitions of q-fractional integral and differential operator together with some basic properties and lemmas are given.In the second chapter,we study the following nonlinear fractional semipositone q-difference system:By using the fixed point theorem in cone,some existence results of the positive solutions are established and an example is given to demonstrate the application of our results.The third chapter studies the following nonlinear fractional q-difference equations with nonlinear integral boundary conditions:nd explores an explicit algorithm which converges to the extremal solutions of the problem at hand.In chapter four,we study the following three-point boundary value problems of nonlinear fractional q-difference equation with p-Laplacian operator:Based on the Bananch's contraction principle,we obtain a sufficient condition for existence and uniqueness of solutions of the problem.By applying the Schauder's fixedpoint theorem,the existence results of solution are obtained.As applications,two examples are presented to illustrate our main results.