Several Types Of Boundary Value Problem For Fractional Differential Equations With Integral Boundary Conditions

Fractional order differential equations with integral boundary value condition is an important branch of application of differential equation.The form of diversification and the scope of application makes it attracted the flock to appreciate and the reseach of scholars.The changes of the times and the rise of economy promote the application of differential equation which inspired generations of scholars soldiers to fight,and then catalytic it step by step toward maturity. It can describe the change rule of somethings and set up the models with such advantage has been widely used in the rheology,and mechanical system,image study,biological medicine,etc.Application of various industeries and discussion of many scholars make it formed different branches.fractional differential equation boundary value problem is one of the important branches of fractional order differential equations.At the same time,there is a weak link behaind these frutiful results in the study of the fractional differential equation boundary value problem,the existence of solution and tow point boundary value.But the research of the fractional differential equations with integral boundary value conditions of boundary value problem still has development.This paper will apply Leggett-Willioms fixed point theorem to the following questions.In this paper,we proved that there are at least three positive solutions to them besed on the fixed point theorem.