New interpolative proximal fuzzy contractions with applications to fractional and thermal models

SANGURLU SEZEN M., Younis M.

Computational and Applied Mathematics, vol.45, no.9, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 9
  • Publication Date: 2026
  • Doi Number: 10.1007/s40314-026-03757-7
  • Journal Name: Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, zbMATH
  • Keywords: Fuzzy metric space, Fuzzy proximal contraction, Two-point BVP, Web-coupling, σ-admissibility
  • Gazi University Affiliated: Yes

Abstract

This study presents interpolative Kannan-type and Ćirić-Reich-Rus-type fuzzy proximal contractions within the context of complete fuzzy metric spaces. We establish several optimal proximity theorems for this novel approximation through the notion of σ-admissibility and derive results that generalize previously recognized findings in fuzzy metric spaces, accompanied by illustrative examples. We utilize our findings to establish the existence of solutions for fractional-order nonlinear differential equations and for two-point nonlinear boundary value problems associated with the thermal radiation of a “satellite-web-coupling,” thereby demonstrating the viability and effectiveness of our methods.