The Existence And Uniqueness Of Solution For Boundary Value Problems For Some Types Of Caputo Fractional Differential Equations (Systems)

Fractional differential equation theory is a branch of the theory of differentialequation and has a wide-ranging applied background in physics, chemistry, controltheory and biology. With the rapid development of science and technology, theresearch about fractional differential equation, especially boundary value problem hasbecome to be recognized as an important research field.Using the fixed point theory and Mawhin’s continuation theorem due to Ge, westudy the existence of solutions of boundary value problems of fractional differentialequations (systems). And thesis contains the following sections:In Section1, we introduce the historical background, some recent results offractional differential equation obtained in the literature and our main work inthis thesis;In Section2, we mainly focus on the study of the existence of solutions ofboundary value problems for a coupled system of fractional differential equationswith p-Laplacian operator, and obtain the existence conditions, which can be provedby fixed point theory of Schauder, our conclusion improved the existing results;In Section3, we discuss the existence of solutions of boundary value problemsfor a coupled system of fractional differential equations with p-Laplacian operator atresonance, and give the existence theorem of solutions with dim KerM=2byextension of Mawhin’s continuation theorem due to Ge;In Section4, we discussed the existence and uniqueness of solution to boundaryvalue problem for fractional differential equations, and our proof depends onscheafer’s fixed point theorem;In Section5, concludes the thesis and future research.This dissertation totally includes55references.