On The Existence Of Solutions Of Fractional Differential Equations With Integral Boundary Conditions

Fractional differential equations have been the research hotspot in recent decades.Due to the fractional order has a better data fitting effect,its theoretical level and application value are constantly improving.In this paper,we mainly focus on the boundary condition problems with integral terms in the boundary value problems of fractional differential equations,and use the tools such as different fixed point theorems to investigate the existence problems.In the first chapter,it shows a brief overview of the research background and significance of Fractional Differential Equations and the research status at home and abroad in recent decades.In the second chapter,it shows the basic knowledge of fractional differential equations to be used in this paper,the basic theory of Banach spaces and the fixed point theorems needed in this paper are briefly introduced.In the third chapter,by using the Leggett-Williams fixed point theorem,we prove that the problem one(in the following form)has at least three positive solutions.Where 2<α<3,0<λ,Dα is the standard Riemann-Liouville fractional derivative,and f:[0,1]×[0,∞]→[0,∞]is a continuous function.In the fourth chapter,we discuss the existence of the solution of problem two(in the folowing form)by using the Krasnoselskii fixed point theorem.Where n-1<α<n,0<ηk<1,λk>0,i=0,1,2,…,n-2,k takes an integer form 0 to m,Dα is the standard Riemann-Liouville fractional derivative,and f:[0,1]×[0,0∞]→[0,∞]isa continuous function.the fifth chapter,this paper briefly summarizes.