The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

中文翻译：

---

扩展b-度量空间中使用定点技术的非线性分数阶微分方程解的存在性

本文的目的是证明扩展b度量空间中循环型算子的不动点定理。还讨论了定点问题的适定性和极限遮蔽性。给出了一些例子来支持我们的结果，并且本文的最后一部分考虑了主要结果的一些应用。本部分的第一部分专门研究边值问题的解决方案的存在。在本节的第二部分中，我们研究了在某些Caputo型分数算子框架中具有整数型边界条件的分数阶边值问题解的存在性。