On extended, and extended rectangular, Menger probabilistic b-metric spaces: applications to the existence of solutions of integral, and fractional differential, equations

We introduce the notions of extended Menger probabilistic b -metric space and extended rectangular Menger probabilistic b -metric space. Thereafter, we obtain new fixed-point results for single-and multi-valued mappings in both spaces. Additionally, we present two applications, involving integral, and fractional differential, equations, proving the existence of solutions.

Automated summary

This article introduces the concepts of extended Menger probabilistic b-metric space and extended rectangular Menger probabilistic b-metric space, and obtains new fixed-point results for single-valued and multi-valued mappings in both spaces. In addition, we present two applications involving integral and fractional differential equations, proving the existence of solutions.