奇异分数阶微分方程积分边值问题正解的存在性

Existence of Positive Solutions for Integral Boundary Value Problems of Singular Fractional Differential Equations

考虑具有Riemann-Stieltjes积分边界条件的Caputo型分数阶微分方程,在允许非线性项奇异的条件下,建立分数阶微分方程Riemann-Stieltjes积分边值问题正解的存在性定理,并运用混合单调算子方法和半序集合上的不动点定理证明存在性定理的正确性.实例表明了所得结论的适用性.

We considered the Caputo fractional differential equation with Riemann-Stieltjes integral boundary condition.We established the existence theorems of positive solutions for the integral boundary value problem of fractional differential equations under the condition of allowing the singularity of the nonlinear term,and proved the existence theorem by using mixed monotone operator method and fixed point theorem on semi-ordered set.Some examples show the applicability of the conclusion.