Fixed point theorems in perturbed supra metric spaces with an application to ABC-fractional foot and mouth disease model

This paper introduces the novel concept of perturb supra metric spaces, which provides a mathematical framework to account for potential errors in distance measurements. We establish several significant fixed point theorems in this generalized setting, including extensions of the Banach’s contraction principle, Kannan type contractions, Chatterjea type contractions, and Reich type contractions. The theoretical results are substantiated with comprehensive examples and applied to analyze a fractional order epidemiological model of Foot and Mouth Disease (FMD) using the Atangana-Baleanu- Caputo derivative operator. Our work demonstrates the robustness of fixed point(FP) theory under measurement perturbations and offers new tools for analyzing nonlinear problems in generalized metric spaces(ms).