带有积分边界条件的分数阶微分方程边值问题正解的存在性

Existence of Positive Solution for BVP of Fractional Differential Equation with Integral Boundary Value Conditions

本文研究非线性分数微分方程边值问题{(cD0,u)(t)+f(t,u(t))=0,t∈(0,1),u(0)=u^(n)(0)=u^(m)(0)=0,u(1)=λ∫10u(s)ds,{其中,α∈(3,4]是该区间上任一实数,^(c)Da为标准的Caputo分数求导结果且f:[0,1]×[0,+∞)→[0,+∞)连续。依托锥上的Guo-Krasnoselskill不动点定理,研究上述边值问题中正解的存在性。

In this paper,we consider the following boundary value problem of nonlinear fractional differential equation{(cD0,u)(t)+f(t,u(t))=0,t∈(0,1),u(0)=u^(n)(0)=u^(m)(0)=0,u(1)=λ∫10u(s)ds,whereα∈(3,4]is a real number,^(c)Dadenotes the standard Caputo fractional derivative,and f:[0,1]×[0,+∞)→[0,+∞)is continuous.By using the well-known Guo-Krasnoselskill fixed point theorem on cones,we obtain the existence of one positive solution for the above problem.