Research On The Solution Of Two Types Of Singular Differential Coupled Systems

Nearly,fractional differential equations have been of increasing importance due totheir diverse applications in science and engineering,so many researchers have shown their interest in fractional differential equations,and the theory have been greatly developed.At the same time,coupled systems of fractional differential equations have received much attention.In this paper,we mainly study positive solutions for two kinds of singular coupled systems of differential equations and it is divided into three chapters.The first chapter introduces the history,evolution and the significance.The second chapter researches a class of coupled system of a second order diiffer-ential equation and a Caputo fractional differential equation as follows where 3<?<4,f(t,x):(0,1)×[0,+?)[0,+?)is a continuous function and may be singular at t = 0,1;g(t,x):(0,1)×(0,+?)[0,+?)is a continuous function and may be singular at t = 0,1 and x = 0.By using fixed point index theorem and building conditions,the existence of the positive solution is obtained.The third chapter researches a class of coupled system of mixed order fractional differential equations as follows where 2<?<3,4<?<5,f,g:<0,1>×[0,+?)?(-?,+?)are continuous functions and may be singular at t = 0,1.By using the fixed point theory of cone and building conditions,the existence of the positive solution is obtained.