Modified version of fixed point theorems and their applications on a fractional hybrid differential equation in the space of continuous tempered functions

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.