Study On Existence And Uniqueness Of Positive Solutions For Boundary Value Problems Of Several Nonlinear Fractional Differential Equations

In this thesis,we consider the existence and uniqueness of positive solutions for boundary value problems of several nonlinear fractional differential equations,specific as follows:In the first chapter,we use the method of mixed monotone operator to consider the existence and uniqueness of positive solutions for boundary value problems of nonlinear fractional differential equations with two nonlinear terms and the bound-ary conditions are integral formswhere <α≤3,1):[0,1]×[0,+∞)2→[0,+∞)is continuous,g:[0,1]×[0,+∞)→[0,+∞)is continuous,q∈C（[0,1],[0,+∞）),CD0+α,D0+β are Caputo fractional derivative.In the second chapter,on the basis of the first chapter,we use the fixed point theorem of increasing （?）-（h,e）)-concave operator to consider the existence and uniqueness of positive solutions for the coupled system dependent on two constants α and bwhere 2<α,β≤3,f,g∈（[0,1]×（-∞,+∞）,（-∞,+∞）） is continuous,q,p∈L1[0,1],α,b are constants,CD0+α,D0+β are Caputo fractional derivative.In the third chapter,we use the Schauder fixed point theorem,Leray-Schauder alternative and Banach contraction mapping principle to consider the existence and uniqueness of positive solutions for nonlinear fractional differential equations coupled systems with integral boundary conditionswhere 2<α≤3,0<λ<Γ（α+1）,f,g∈C（[0,1]×R×R,R）,D0+α,D0+β are Riemann-Liouville fractional derivative.