Modular Suprametric Spaces and Fixed-Point Principles with Applications in Fractional Burn-Healing Dynamics

We introduce a new nonlinear distance structure, a modular suprametric space, that integrates modular metrics with perturbations characteristic of suprametrics. Within this framework, we develop a contraction principle tailored to its nonlinear geometry and demonstrate the existence of fixed points under a generalized iterative control. In order to showcase the practical application of this proposed structure, we analyze a burn-healing model driven by nonlinear recovery dynamics. The derived fixed-point conditions ensure both the existence and stability of the healing equilibrium. Our findings indicate that modular suprametric spaces serve as a versatile analytical tool for dynamical systems whose evolution exhibits nonstandard sensitivity, saturation effects, or exponential response behavior.