Study On Solvability For Boundary Value Problem Of Several Fractional Differential Equations

This paper studies the solvability of boundary value problems of several non-linear fractional differential equations,specific as follows:In the first chapter,by using the method of Leray-Schauder continuation the-orem to study the solvability for boundary value problems of nonlinear fractional differential equations where 2<a≤3,f:[0,1]× R3→R is continuous,cD0a+is Caputo fractional derivative.In the second chapter,by using Mawhin continuation theorem to consider the existence of solutions for boundary value problems of nonlinear fractional differential equations with nonlinear boundary conditions where f:[a,b]× R ×R→R,gi:R× R→R,i= 1,2 is continuous.In the third chapter,by using Banach’s contraction principle and Schaefer’s fixed point theorem,we consider the existence and uniqueness of solutions for the boundary value problems of nonlinear fractional differential equations on star graph where 2<α≤3,0<β ≤1,cD0,x,α,cD0,xβ is a Caputo fractional derivative,fi,i=1,2,…,k,is a continuous function on[0,1]×R×R.