Existence Of Positive Solutions For Several Tow-Point BVP With Nonlinear Fractional Differential Equation

It’s very important to research on the existence of positive solutions of boundary value problems for differential equations, because you can not begin the next step of work for seeking the numerical solutions and applying into practice, such as inspection, control and prediction of the practical problems, unless we make clear whether and how many solutions exist. Therefore, the study to the existence of solutions of boundary value problems, especially the existence of positive solutions, by means of the methods of nonlinear functional analysis arises recent decades years, has greatly attracted many mathematics workers’attention.In this paper,we study two kinds of two-point boundary value problems for nonlinear fractional differential equations:1.Nonlinear Riemann-Liouville boundary value problem Where D0+α is the standard Riemann-Liouville fractional derivative and3<α≤4is a real number,f:[0,1] x [0,+∞) is continuous.2.Nonlinear Caputo boundary value problem Where cD0+α is the Caputo fractional derivative and2<α≤3is a real number, f:[0,1]×[0,+∞) is continuous.