Studies On The Existence Of Solutions For Fractional Differential Equations

This paper is concerned with the existence of solutions for fractional differential equations, including four chapters. The main results are in chapter2and chapter3.In chapter2, a class of fractional differential equation with integral boundary value conditions is investigated. By using the Schauder fixed-point theorem, some sufficient conditions are established to guarantee the existence of positive solutions for this kind of problems, which improve the known results. Furthermore, some examples are given to illustrate the advantages of the results.In chapter3, the initial value problems of fractional functional differential equations are studied. By using the Schauder fixed-point theorem, some sufficient conditions are established to guarantee the existence of solutions for this kind of problems. Furthermore, we extend the continuation theorems for ordinary differential equations to the ones for fractional functional differential equations.