This article contains modified version of fixed point theorems with the help of freshly made contraction operators and the solvability of a fractional hybrid differential equation involving Caputo fractional derivative by using modified Darbo’s fixed point theorem in the space of continuous tempered functions. The fundamental tool used in the solvability of the fractional hybrid differential equation is the measure of noncompactness approach. Our results indicate the importance of fixed point theorem for finding solutions of the fractional hybrid differential equation and improve some known results, which have wider applications as well. Also, there are two suitable examples are given to illustrate our results.

本文包含借助于新制作的收缩算子的不动点定理的修改版本，以及通过在连续调和函数空间中使用修改的 Darbo 不动点定理来求解涉及 Caputo 分数阶导数的分数混合微分方程的可解性。分数式混合微分方程可解性中使用的基本工具是非紧性方法的度量。我们的结果表明了不动点定理对于寻找分数混合微分方程的解的重要性，并改进了一些已知的结果，这些结果也具有更广泛的应用。此外，还给出了两个合适的例子来说明我们的结果。