A Class Of Existence Of Multiple Positive Solutions For Boundary Value Problem For Fractional Difference Equations

The fraction differential equation is an important branch of ordinary dif-ferential equation. The fractional order nonlinear differential equation boundary value problem is also the hot spot which has been discussed in recent years. In this paper, we use the fixed point theory, as well as cone expansion and com-pression theorem to investigate a class of the existence of positive solutions for the fractional boundary value problems involving with Caputo derivative, mean-while, we also investigate two sorts of the existence of positive solutions for the fractional boundary value problems involving with Riemann-Liouville derivative. This dissertation contains three chapters.Chapter1Investigates a class of two-point boundary value problem for non-linear fractional differential equations with the form of Caputo derivative, by using the Krasnoselskii fixed point theorem and Leggett-Williams fixed point theorem, existence of multiple solutions for the fractional differential equations with two-point boundary value problem are obtained.Chapter2Studies a nonlinear fractional differential equation with Riemann-Liouville derivative by means of a two-cone generalized fixed-point theorem, an existence result of triple positive solutions for two-point boundary value problem of nonlinear frac-tional differential equation is obtained. Chapter3The following nonlinear fractional boundary value problem is considered we obtain the existence results of positive solutions by applying Leray-Schauder nonlinear alternative theorem and give the uniqueness of positive solution by means of Banach contraction mapping principle.