Existence And Uniqueness Of Solutions For Two Class Of Boundary Value Problems Of Fractional Differential Equations

The dissertation is most concerned with the existence and uniqueness of solutions for two classes of boundary value problems of fractional differential equations. By the use of the fixed point theorem and the contraction mapping principle, the existence and uniqueness of solutions are given under the suitable conditions. This dissertation is divided into three parts.In Chapter1, the development of differential equations, fractional differential equations is specially introduced. The preliminary knowledge which is relevant to the paper is given. The main conclusions are also presented.Chapter2is concerned with the existence and uniqueness of solutions of three-point boundary value problems for fractional differential equations where1<a≤2,0<a<1,0<b<1,η∈(0, T), f:J×R×Râ†'R, and S is the first Fredholm integral operator, defined by where k∈(J×J, R+). At last, two sufficient conditions are obtained by the use of the Schaefer fixed point theorem.In Chapter3, we consider the existence and uniqueness of solutions of multi-point boundary value problems for fractional differential equations where cD0+α,CD0+β are the standard Caputo derivative,f:[0,1]×R×Râ†'R. We study the equations by the use of the Schauder fixed point theorem. The existence and uniqueness of solutions are given under the suitable conditions. Two examples are given to illustrate the results.