The Research About Existence Of Positive Solutions For Three Types Of Boundary Value Problems Of Fractional Differential Equations

The theory research about fractional differential equations has been of great interest in the recent half a century.It is caused by both the intensive development of the fractional calculus theory and the wide applications.Some fractional equation model have been widely used in the scientific fields,such as economic,chemistry,biology,physics,medical science,and so on.Thus,the solvable fractional equation model from the special academic research can make a great difference in the modern society.In this paper,we mainly investigate the existence of positive solutions for three types of fractional differential equations.Firstly,we use iterative skill and0 u positive operator to investigate the uniqueness of iterative positive solution for the following multi-point boundary value problem of fractional differential equation:we get the conclusion that if the function f(t,u(t))satisfies Lipschitz conditions,then we can get the existence and uniqueness of positive solution when the Lipschitz constant satisfies certain conditions.Secondly,we investigate the following multi-point boundary value problem of fractional differential equation with p-Laplacian:In the paper,we discuss the range of parameter l,we use Guo-Krasnoselskii fixed point theorem to investigate the existence and non-existence of positive solutions.Finaly,we study the following singular p-Laplacian fractional differential equations boundary value problem:we deal with the singularity by proving the existence of positive solution for a modified fractional differential equation.The proof is based on upper and lower solutions and Schauder fixed point thorem.