Boundary Problems For Fractional Differential Equation With P-Laplacian Operator

In recent years, nonlinear fractional differential equations have been widely used in many fields, and the boundary value problem of nonlinear fractional differential equations is a class of important problem in differential equations. With the deepening of the re-search and more and more results have emerged, nonlinear fractional differential equations occupy more and more proportion, but among many branches of differential equations,the boundary value problem of the research is especially important, which still needs to be further supplemented and needs to be further studied.In the second chapter, we discuss the existence and uniqueness of positive solution-s for the following two points boundary value problems of fractional order differential equations with p-Laplacian operator.where ?p is the p-laplacian operator; ? ? (1,2),? ?(0,1),D0+?,D0+?+ is the standard of Riemman-Liouville fractional derivative, f is the continuous function.In the third chapter, we discuss the existence of positive solutions for the following two points boundary value problems of fractional order differential equations with p-Laplacian operator.where 1<??2,0<??1. D0+? is the standard of Riemann-Liouville fractional derivative. And f is the continuous function, ?p is the p-Laplacian operator.In the above chapters, we first discuss some properties of the p-Laplacian operator on the nonnegative bounded interval and discuss the relationship between the bounded sets and bounded sets, after for the given the proper condition of nonnegative function a and nonlinear function f, combined with the Green function which conversing from differential equations into integral equations, we used the method of measure of noncompactness and fixed point theorems to give the criterion of existence and uniqueness of positive solutions for the above problems.