Positive Solutions For A Class Of Fractional Differential Equations With Nonlocal Boundary Value Problems

In this thesis, we investigate the existence of positive solutions of multipoint boundary value problems and integral boundary value problems of fractional differential equations with parameters. This thesis includes five chapters.In the first chapter, we introduce the fractional differential equation's re-search background and the main results of the thesis.The second chapter, some basic definitions and lemmas are given to be used in this thesis.The third chapter is mainly concerned with the existence of positive solu-tions of multi-point boundary value problems of Riemann-Liouville type frac-tional differential equations with parameters. By using Krasnosel'skii's fixed point theorem, we first derive the sufficient conditions for the existence of at least one positive solutions of the boundary value problem with parameters; and then establish the sufficient conditions of the existence of at least three posi-tive solutions of the boundary value problem with one parameter by Leggett-Willimas fixed point theorem. Finally, an example is given to illustrate the application of the obtained result.In chapter four, we study positive solutions for a class of boundary value problems of Caputo type fractional differential equations with integral boundary condition. By virtue of Schauder and A very-Peterson fixed point theorem, we obtain the sufficient conditions for the existence of at least one and three positive solutions of the boundary value problem,respectively.In chapter five, we propose some ideas to be developed for the problems related to this thesis. All the results of this thesis improve and extend some existing results.