Research On Boundary Value Problems Of Fractional Differential Equations

In recent years, the research of fractional differential equations has made a lot of new achievements, but because of its wide application, we still need to do further research.This paper discusses the boundary problems of fractional differential equations with Riemann-Liouville derivative and Caputo derivative. Through studying the properties of the Green function, we obtain some important conclusions. In the second chapter, by mainly using the Guo-Krasnosel'skii fixed point theorem, we research the existence of positive solution when ? is in different conditions, and give two cases without solution. In the third chapter, by using the Banach contraction mapping principle and the Krasnosel'skii fixed point theorem, we prove the existence and uniqueness of solution. Besides, by using the Guo-Krasnosel'skii fixed point theorem and the Leggett-Williams fixed point theorem, we discuss the existence and multiplicity of positive solutions.