The Research For Nonlocal Boundary Value Problems Of Fractional Diferential Equations

Fractional diferential operators are nonlocal and represent systems with memory. Theproperties of fractional diferential operators are sufcient to describe practical situation.Therefore, we make scientific researches on the nonlocal boundary value problems of dif-ferential equations which are provided with important theoretical significance and practicalvalue. The text consists of six chapters.In chapter one, we present the research background, present situation and main results ofthis thesis.In chapter two, the preliminaries of this thesis are introduced, such as the definition andproperties of fractional derivatives and integral, the theory of cone, the method of partialordering, Leray-Schauder degree, the Kuratowski measure of noncompactness, the theoremof fixed points and so on.In chapter three, we focus on the multiple solutions for fractional diferential equationswith nonlinear three points boundary value conditions which include periodic boundary value,anti-periodic boundary value conditions, by means of the Amann theorem and the theory ofcone and the method of upper and lower solutions. Therefore, we extend some previous resultsin many respects.In chapter four, we prove tectonically the existence of the nonlocal boundary value prob-lem for fractional diferential equations by Leray-Schauder degree.In chapter five, we devote our attention to the solution of the nonlocal boundary valueproblem for fractional diferential equations in a Banach Space, by means of the concept ofmeasures of noncompactness and the fixed point theorem of Mo¨nch type. It is in this aspectthat our work fills up the deficiency which is developing slowly.In chapter six, we are concerned with the nonlocal boundary value problems of extrem-ist solutions for first order impulsive integro-diferential equations with deviating argumentswhich are the special case of fractional diferential equations, by establishing a new compar-ison principle and using of the monotone iterative technique and the method of upper andlower solutions.