Existence Of Solutions For Boundary Value Problems Of Some Fractional Differential Equations

Fractional order calculus is a classical generalization of integer order calculus,which can better describe some complex practical problems in real life.In recent years,the fractional differential equation boundary value problem has attracted much attention.In this paper,the existence of solutions for boundary value problems of three kinds of fractional differential equations are discussed by using continuity theorem and fixed point theorem.This paper is divided into five chapters:Chapter one,the introduction,mainly introduces the research background,research status,the main work of this paper and some preliminary knowledge.Chapter two,the existence of solutions for a class of fractional coupled differential systems with Riemann-Stieltjes integral conditions at resonance conditions is studied by using continuity theorem.The existence theorem of solutions is established.The boundary value problem of a single equation is extended to a coupled system,and the boundary value condition is more general.Chapter three,the existence of solutions for periodic boundary value problems of a class of implicit fractional-order coupled differential systems is studied by using the continuity theorem,and sufficient conditions for the existence of solutions are given.Chapter four,the existence of solutions for Hadamard type fractional differential equation boundary value problems with integral boundary conditions on infinite intervals is studied by using fixed point theory,and the results of the existence of solutions are obtained.Compared with the existing work,the problems discussed are more general.Chapter five,summarizes and prospects,mainly summarizes the innovation points of this paper and makes a tentative plan for the follow-up discussion.