In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions $f(t,u,v)$ and $g(t,u,v)$ in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann–Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green’s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.

中文翻译：

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Riemann-Stieltjes耦合积分边值条件的一类非线性奇异分数阶系统的正解

在本文中，利用Banach空间中的Riemann–Stieltjes耦合积分边值条件，推导了确保一类非线性奇异分数阶微分系统正解存在和多重性的充分条件。非线性函数$F（Ť，ü，v）$ 和 $G（Ť，ü，v）$在考虑的系统中，每个变量都可以是奇异的。此处的边界条件是带有黎曼–斯蒂尔杰斯积分的耦合形式。为了克服由奇异性引起的困难，通过与系统相关联的格林函数的性质来构造合适的圆锥体。本文使用的主要工具是圆锥上的不动点定理。最后，提供一个例子来说明我们获得的新结果的有效性。