Hardy-Rogers Type Interpolative Contractions in Fuzzy Strong \(b\)-Metric Spaces with Application to a Duffing Oscillator

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DOI: https://doi.org/10.28924/2291-8639-24-2026-287
Published: Sep 21, 2026
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Mohammad Akram, Fahad Jahangeer, Tayyab Kamran, Umar Ishtiaq, Ioan-Lucian Popa, Hardy-Rogers Type Interpolative Contractions in Fuzzy Strong \(b\)-Metric Spaces with Application to a Duffing Oscillator, Int. J. Anal. Appl., 24 (2026), 287.

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Mohammad Akram, Fahad Jahangeer, Tayyab Kamran, Umar Ishtiaq, Ioan-Lucian Popa

Abstract

We study fixed point theory in fuzzy strong \(b\)-metric spaces for a class of interpolative contractions driven by a pair of auxiliary functions \((\Upsilon,\digamma)\). After recalling the necessary background, we introduce Banach, Kannan, Chatterjea, Reich-Rus-Ciric, and Hardy-Rogers type fuzzy strong \(b\)-interpolative contractions and establish existence and uniqueness of fixed points for the corresponding \((\Upsilon,\digamma)\) versions. A recurring theme is that these contractions are strictly weaker than their classical analogues: for each type we exhibit a mapping that satisfies the interpolative condition while violating the classical one, and we identify explicitly the range of the contraction parameter over which the classical inequality fails. As an application, we recast a modified Duffing oscillator as a nonlinear Volterra integral equation of the second kind and use the Hardy-Rogers \((\Upsilon,\digamma)\) theorem to prove that it admits a unique continuous solution. We also derive a geometric a posteriori error bound for the associated Picard iteration, and numerical experiments together with phase-space diagrams illustrate both the convergence and the underlying nonlinear dynamics.

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