Existence Of Solutions For Boundary Value Problems Of Nonlinear Fractional Differential Equation

Fractional differential equations have gained considerable importance due to their application in various science, many mathematical modelings in various science are described on basis of fractional differential equation. Boundary value problem and initial value problem of fractional differential equation has developed very rapidly. With the further study of this direction, the study contents and methods continuously get abundant. A lot of results have been obtained for fractional equations. However, there are still many area which can be developed for less results about Boundary value problem of nonlinear fractional differential equations.This paper discusses the boundary value problems for two class of fractional differential equations with Riemann-Liouville derivative. In the second chapter, by introducing stochastic variable, we get the solution for a kind of nonlinear fractional differential equations. In the third chapter, we chance the boundary value conditions from real to fractional, and get the solution for nonlinear fractional boundary value problems at resonance with new conditions.