The Nature Of The Two Types Of Fractional Differential Equations,

This dissertation studies the existence and uniqueness solutions of fractional differential equations with irregular boundary conditions and existence solutions of coupled systems by using the Schauder fixed point theorem, the Banach contraction mapping principle, the fixed point theorem in cones and the Leray-Schauder fixed point theorem. We obtain a series of results on the some known results in the existing references. This dissertation is divided into four chapters. The main contents are as follows:In the first Chapter, we introduce the historical background and the up-to-date progress of the fractional differential equations as well as the main results of this paper.In Chapter 2, we discuss the preliminary definitions and theorems of the fractional differential equations as well as the ones associate with the issue we investigate.In Chapter 3, we consider the following fractional differential systemWe assume that the fractional differential equation satisfies some given conditions. Under these assumptions, some meaningful results on the existence and uniqueness solutions are obtained by using the Schauder fixed point theorem and the Banach contraction mapping principle.In Chapter 4, we consider the following coupled system of fractional differential equation We extend the single system to a coupled system, using the fixed point theorem in cones, the Schauder fixed point theorem and the Leray-Schauder fixed point theorem, the results obtained enrich the ones in chapter 2.