The Existence Of Positive Solutions For Several Types Of Fractional Differential Equations

Fractional differential equations are the continuation and extension of integer-order differential equations.Fractional calculus and integer calculus are unified.However,when people enter the study of complex systems and complex phenomena,classical integer-order differential equations are no longer convenient and feasible.In recent decades,the theory of fractional differential equations has been continuously developed and improved.At the same time,more and more people apply it to fractional physics,chaos and turbulence,viscoelastic mechanics and non-Newtonian fluid mechanics,and the solution of polymer materials.Chains and other different areas.In the field of mathematics,more and more scholars have studied it further.The existence of positive solutions of fractional differential equations is an important research direction.In this paper,the existence of positive solutions of several fractional order differential equations is studied in four chapters.The first chapter is the introduction.This paper mainly introduces some definitions,lemma,theorems used in fractional order differential equations.The second chapter considers the existence of positive solutions of fractional semipositone differential equations with integral boundary conditions.In this note,according to the properties of green function,the existence of positive solutions is obtained by using Leray-Schauder alternative theorem and the Guo-Krasnoselskill?s fixed point theory.The third chapter considers the uniqueness of positive solution for fractional differential equation with parameter integral boundary value condition.In this note,according to the properties of green function,the uniqueness of positive solutions is obtained by using fixed point theory.The forth chapter considers the existence of positive solutions for fractional order differential equations with integral boundary value conditions.This note studies existence of the positive solution of the Guo-Krasnoselskill?s fixed point theory is obtained by using the height function.