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

Paunović M., Büyükkaya A., Öztürk M.

Mathematics, vol.14, no.7, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 7
  • Publication Date: 2026
  • Doi Number: 10.3390/math14071208
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, Directory of Open Access Journals
  • Keywords: burn-healing dynamical model, fixed-point theory, fractional integral equations, generalized contraction mappings, modular suprametric spaces
  • Karadeniz Technical University Affiliated: No

Abstract

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.