Nonlocal Problems Of Fractional Differential Equations

For the nonlocal boundary value problems of fractional evolution equations,we obtain the existence of mild solutions in the cases that the semigroup is compact and noncompact,respectively.This paper is concerned with the nonlinear and nonlocal boundary problems of a class of fractional differential equations with Caputo derivatives.In chapter 2,we firstly study the form of mild solutions for initial boundary value problem of the fractional evolution equation,to obtain the definition of mild solutions,and define a solution operator?:?(?)D,which maps the initial value u0 ?? to the set of the mild solutions for initial boundary value problem.Then the nonlinear nonlocal problem is equivalent to an abstract inclusion of F(u0)? ?(?(u0)).Then we obtain the existence of mild solutions in the case that the semigroup is compact,by using the homotopy invariance of Benevieri-Furi degree theory.In chapter 3,we use the method of noncompact measures to acquire the existence of mild solutions for nonlinear and nonlocal problem when the nonlinearity f satisfies the Lipschitz continuous condition.In the case that the semigroup is noncompact.