In the current article we obtain the extension of Darbo’s fixed point theorem (DFPT), and apply this theorem to prove the existence of solution of an infinite system of implicit fractional integral equations. We, besides that, justify the results with the help of an example. The advantage of the proposed fixed point theory is that the requirement of the compactness of the domain is relaxed which is essential in some fixed point theorems. Also, we have applied it to integral equation involving fractional integral by another function which is a generalization of many fixed point theorems as well as fractional integral equations.

中文翻译：

---

广义Darbo不动点定理的无穷分式积分方程组的存在性。

在本文中，我们获得了Darbo不动点定理（DFPT）的扩展，并应用该定理证明了隐式分数阶积分方程的无穷大系统解的存在性。除此之外，我们还借助示例来证明结果的合理性。提出的不动点理论的优点是放宽了对域的紧缩性的要求，这在某些不动点定理中是必不可少的。同样，我们通过另一个函数将它应用于涉及分数积分的积分方程，该函数是许多定点定理以及分数积分方程的推广。