The Basic Theory Of Fractional Differential Equations And Their Application

In this thesis,some basic theories of the fractional differential equation are dis-cussed,including global existence and uniqueness of solution for initial value problems,sufficient and necessary conditions of continuable solution,the estimated growth of so-lution and the existence of boundary value problem in half axis at resonance.Recently,the existence and its related properties of solution for the various types fractional dif-ferential equations is a research subject of great practical and theoretical significance,which has received considerable attention,and much significant work has been carried out by many authors.In this paper,some new approaches are greatly developed to deal with weak singularity,half space and resonance conditions,obtaining some theo-rems which guarantee the existence of solution under relatively weak assumptions and are easily applied to verify whether the solution is continuable or not,via introducing the newly complete Banach space construed,modified Ascoli-Arzela compactness cri-terion and a new projection operator.With the aid of preprocessing multiple-valued operator,Riesz representation theorem and bounded variation functions,some suffi-cient conditions under which the existence of solution can be guaranteed for fractional integro-differential inclusions and fractional functional differential equations are ob-tained.Furthermore,some specific necessary examples are also given to demonstrate the applicability of the previously derived theoretical results.