Fixed point results in Menger probabilistic suprametric spaces with an application to fractional differential equations

In this paper, our objective is to extend the concept of Menger probability metric space by presenting its corresponding structure, namely the Menger probability suprametric space. Additionally, we investigate several topological properties of this space and establish a fixed point theorem involving probabilistic nonlinear Banach contractions. As applications, we present a suprametric extension of (Mediterr. J. Math. 19(5):1–18, 2022) and a consideration of the solution existence of a fractional differential equation that involves ψ-Hilfer fractional derivatives.