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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Müzeyyen Sangurlu Sezen,
  • Mudasir Younis

摘要

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 \(\sigma \) 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.