Research On The Existence Of Solutions Of Two Types Of Fractional Differential Equations

In recent years,with the rise of emerging technologies such as quan-tum mechanics in physics,artificial intelligence in computer science and data mining,people have conducted in-depth studies on these emerging technologies and found that many problems can be turned into a va-riety of nonlinear problems.In the process of solving these non-linear problems,a non-linear functional analysis branch with the contents of the semi-order method,topological method,and variational method is gradually formed.In view of the nonlinear differential equations in the-ory and in practice.The significance of the nonlinear functional analysis branch has long been favored by many researchers.Fractional calculus is a theory about the differential and integral of ar-bitrary order,which is the generalization of integral calculus.At present,the theory of integral calculus is quite mature.And the mathematical models of many problems can be attributed to the solution of integral d-ifferential equations.In recent years,the fractional differential equations that are abstracted from practical problems have drawn the attention of researchers in mathematics,for[20-30].This paper mainly studies the existence of solutions for several kinds of fractional differential equations,which are divided into three chapters altogether.The first chapter introduces the background knowledge of fractional differential equations which are used later.The second chapter studies the following infinite boundary value problemIn this chapter,the existence and uniqueness of positive solutions are obtained by using the fixed point theory of operators.The third chapter studies the following fractional differential equa-tionsSuppose the following conditions are met:(?),among them among them (?)among them (?).The existence of positive solutions is obtained by using the fixed point index theorem on cones.The following conditions are satisfied:(H7)h((0,1),[0,+?))Is continuous and satisfies that any subinterval of interval(0,1)is not always zero;(H8)For any positive number r1<r2,there is a continuous function:(?).The existence of positive solutions is proved by the height function.