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<α≤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<λ<Γ(α+1),α∈(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(?) whereγ=Γ(α+1)is the resonance condition for the above problem,α∈(1,2],f:[0,1]×R2→R satisfies Caratheodory condition.