Existence And Uniqueness Of Positive Solutions For A Class Of Nonlinear Fractional Differential Equations With Integral Boundary Condition

In the thesis,we study a class of nonlinear fractional differential equations with integral boundary conditions:where 1<? ? 2 is a real number,D0?+ is the standard Riemann-Liouville differentiation,f:[0,1]x[0,?)?[0,?)is continuous,and g(t)? L1[0,1]is nonnegative.In Chapter 1,we give the fundamental definition and basic properties of Riemann-Liouville fractional calculus,and derive the corresponding Green func-tion and its properties.In Chapter 2,we discuss the existence and uniqueness of a positive solution to the BVP by means of Banach Fixed Point Theorem.And some new results on the existence of multiple positive solutions for the boundary vale problem are obtained in Chapter 3,using Leggett-Williams Fixed Point The-orem.We give four examples in Chapter 4 to demonstrate the application of our theoretical results.