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

• Published in: Fixed point theory and algorithms for sciences and engineering Vol. 2025; no. 1; pp. 5 - 24
• Main Authors: Chaira, Karim, El Harmouchi, Nour-Eddine
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 08.04.2025; Springer Nature B.V; SpringerOpen
• Subjects: Algorithms; Analysis; Applications of Mathematics; Differential equations; Differential Geometry; Fixed point; Fixed points (mathematics); Fractional calculus; Mathematical and Computational Biology; Mathematical functions; Mathematics; Mathematics and Statistics; Menger probabilistic metric space; Menger probabilistic suprametric space; Metric Fixed Point Theory and Its Applications; Metric space; Norms; Statistical analysis; Suprametric space; Topology; ψ-Contraction; Menger probabilistic metric space; Metric space; Hilfer fractional derivative; Menger probabilistic suprametric space; Hilfer fractional differential equation; Contraction; Fixed point; Suprametric space
• ISSN: 2730-5422; 2730-5422
• DOI: 10.1186/s13663-025-00782-9

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.