Study On Existence Of Positive Solution Of Several Fractional Differential Equations

In this thesis,we discuss the solvability of several fractional differential equa-tions.The main results are:In chapter 1,by using fixed point theorem of Krasnosel'skii,we study the existence of positive solutions for the singular higher-order fractional differential equation semipositone problem(?) where n-1<??n,n?2,q(t)?C[0,1]and q>0,f?C([0,1]×(0,+?)×Rn-2,R),f may be singular at u=0.In chapter 2,by using fixed point theorem of Leggett-Williams,we study the existence and multiplicity of positive solutions for the fractional differential equation with a class of integral boundary value condition(?) where 0<?<?(?+1),??(2,3],f:[0,1×[0,??)?[0,+?)is continuous.In chapter 3,by using Mawhin contiouation theorem,we study the existence solution for the fractional differential equation with a class of integral boundary value condition at resonance(?) where?=?(?+1)is the resonance condition for the above problem,??(1,2],f:[0,1]×R2?R satisfies Caratheodory condition.