| Fractional evolution equations play a very important role in terminal value problems and control theory.Compared with integer differential equations,they can more accurately describe their actual states in chemical and physical problems.The main content of this paper is to study the terminal value problem of a class of fractional evolution equations with Liouville-Weyl derivative in infinite interval and the exact controllability of a class of fractional evolution equations with ψ-Hilfer.In chapter 2,we first study some important properties of ψ-Hilfer fractional derivative,then use its properties to transform the differential equation into an equivalent integral equation,and then carry out a generalized Laplace transform on the product decomposition.On this basis,we use the method of compact operator approximation and the lemma of some noncompact measures to obtain the compactness of the operator.Finally,we obtain the exact controllability of the system(2.1)according to Schauder fixed point theorem.In Chapter 3,in a given space,the differential equation is similarly transformed into an integral equation on an infinite interval by using some important properties of Liouville-Weyl derivative.On this basis,some useful auxiliary conditions are assumed,and then through the generalized Arzela-Ascoli theorem,Schauder fixed point theorem.Then,the existence of(3.1)moderate solution of the system is obtained,The previous results in this chapter are generalized. |
