Study On The Basic Theory Of Fractional Differential Equations

With the fractional order differential equations are widely used in various fields,study on the theory of fractional differential equations has become a popu-lar topic and obtained many achievements.This paper deals with on the existence and uniqueness of solutions for fractional differential equations.In chapter 3,a class of initial-value problems for fractional neutral functional differential equations is investi-gated.By employing Schauder fixed point theorem and Banach contraction mapping principle,some sufficient conditions are obtained to guarantee the existence and unique-ness of solutions for such problems.In chapter 4,it is concerned with the two-point boundary value problem to a coupled system of fractional differential equations.By applying Kolmogorov-Riesz theorem and Schauder fixed point theorem,some sufficient conditions are given to guarantee the existence of solutions for this kind of problems in LP Space.