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<p>This research introduces a cogent algorithm for quantifying the one-dimensional fractional Rayleigh-Stokes model using an orthonormalized Detour polynomials (ODPs) accessible matrix. The Caputo fractional derivative functions to compute the time derivative. The fractional Rayleigh Stokes equation is then translated into a set of nonlinear algebraic equations using prevalent collocation sites. The resulting structure is handled using Newton's methodology to accomplish the proposed Detour polynomial collocation approach (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb{D}}{\mathbb{C}}{\mathbb{A}}\)</EquationSource> </InlineEquation>). The scientific method has the added benefit of including orthonormal Detour polynomials and operational matrices, which shortens the processing time and optimises speed. In addition, we are offering four empirical examples that evaluate the credibility of the unique technique, as well as computational experiments that illustrate its utility and accuracy.</p>

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A Detour Polynomial-Based Graph Framework for Solving (1 + 1) Dimensional Fractional Rayleigh–Stokes Equations

  • 期刊论文

  • 发表日期：

    2026年7月17日

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  • A. N. Nirmala,
  • S. Kumbinarasaiah

摘要

This research introduces a cogent algorithm for quantifying the one-dimensional fractional Rayleigh-Stokes model using an orthonormalized Detour polynomials (ODPs) accessible matrix. The Caputo fractional derivative functions to compute the time derivative. The fractional Rayleigh Stokes equation is then translated into a set of nonlinear algebraic equations using prevalent collocation sites. The resulting structure is handled using Newton's methodology to accomplish the proposed Detour polynomial collocation approach ( \({\mathbb{D}}{\mathbb{C}}{\mathbb{A}}\) ). The scientific method has the added benefit of including orthonormal Detour polynomials and operational matrices, which shortens the processing time and optimises speed. In addition, we are offering four empirical examples that evaluate the credibility of the unique technique, as well as computational experiments that illustrate its utility and accuracy.