Extermal Solutions For Nonlinear Fractional Differential Equations With Infinite-point Integral Boundary Conditions

In recent years,fractional order calculus has been playing a more and more important role in many fields,and it has become the focus of research in many mathematical fields.And the existence and uniqueness of the solution have become the main research object.In this article,the first chapter introduces the research background of fractional differential equations.The second chapter introduces the existence of extremal solutions for a class of fractional differential equations:where 2<α,β≤ 3,u(t),v(t),∈[0,1],f,g:I × R→R are continuous.Dα,Dβ,Iα Iβ are the standard Riemann-Lionville fractional differential operator.Based on this,the third chapters use the monotone iterative techniques and upper and lower solutions,and then we study the following nonlinear fractional differential equations with infinite-point integral boundary conditions:where α>2,β ≥ 0,i ∈[0,n-2]is a fixed integer,αj≥ 0,0<ξ1<ξ2<...<ξj-1 ＜ξj＜...<1(j = 1,2,...),△-Σj=18Γ(α+β)Γ(α)αjξjα+β-1＞0,D0+α is the standard Riemann-Liouville fractional differential operator.