Existence Of Solutions To Boundary Value Problems Of A Class Of Fractional Differential Equations

In this paper,we consider the existence of positive solutions for the following nonlinear fractional differential equations with boundary conditions,it is divided into three chapters.The first chapter introduces the history and evolution,and the relevant definitions are given.The second chapter researches the existence and uniqueness of positive solutions for the following nonlinear fractional differential equations with boundary conditions:????2.1.1?where n-1<??n,n?3,D₀₊^? is the standard Riemann–Liouville derivative.By using the properties of the the fixed point theory,and Green function under some conditions with respect to the relevant linear operator,we obtain existence results of positive solution.The third chapter researches the existence and uniqueness of positive solutions for the following nonlinear fractional differential equations with boundary conditions:????3.1.1?where n-1<??n,n?3,??[1,n-2],0??_i,?_i?1,1-^?_i=1??_i?_i^?-?-1>0,D₀₊^? is the standard Riemann–Liouville derivative.By using the properties of the Green function,and the concave operators theory under some conditions with respect to the relevant linear operator,we obtain existence and uniqueness results of positive solution.