Existence Of Solutions For Boundary Value Problems Of T Kinds Of Fractional Differential Equations With P-Laplacian Operator

Fractional calculus theory is the generalization of the traditional integer calculus theory.It has been more than three hundred years since it was put forward.Especially in recent decades,it has been studied by a lot of scholars,and many important results have been widely used in physics,engineering,machinery,medicine,biology and many other scientific fields.P-Laplacian operator is derived in many practical problems,but the fractional differential equation boundary value problem with p-Laplacian operator is relatively complicated and the research on its existence of the solutions is more difficult,so the theoretical results are relatively few.The present paper is inspired by the results of the study on the fractional differential equation boundary value problem with p-Laplacian operator by many domestic and overseas scholars,and devoted to the study of the existence of solutions for boundary value problems of two types of nonlinear fractional differential equation with p-Laplacian operator.First of all,we obtain the sufficient condition of three positive solutions of three-point boundary value problems for fractional differential equations with p-Laplacian operator by the Avery-peterson fixed point theorem.Secondly,by using the related fixed point theorem,we obtain the sufficient condition that the boundary value problems of fractional differential equations with p-Laplacian operator have at least one positive solution.At last,we obtain the sufficient condition of at least one solution for multipoint boundary value problems of fractional differential equation with p-Laplacian operator and integral boundary conditions by using the Schauder fixed point theorem.