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<p>In this work, we study linear systems with deformable derivatives and provide a matrix-based approach to their solution. The given system is first transformed into a comparable classical matrix differential equation using a deformation-adjusted system matrix. This allows us to use popular techniques like the Putzer algorithm &amp; the Cayley-Hamilton theorem to generate explicit solutions. One advantage of this approach is that it doesn’t need eigenvector calculation or diagonalization. To illustrate the method, we look at two scenarios: a radioactive decay-growth scenario and a mortgage payback issue. The findings demonstrate that, for linear constant-coefficient systems, the deformable framework introduces a single parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\theta\)</EquationSource> </InlineEquation> that modifies the effective evolution rate. Although the present analysis is confined to two elementary applications, the numerical experiments suggest that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\theta\)</EquationSource> </InlineEquation> can be tuned to mimic delayed responses without increasing computational complexity – a feature that may prove useful in domains where fractional models are too heavy.</p>

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Matrix-based solution methods for deformable derivative systems: applications to growth-decay and mortgage models

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月13日

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  • Komal Priya,
  • Mohammad Ayman-Mursaleen,
  • Amit Ujlayan,
  • Nadeem Rao

摘要

In this work, we study linear systems with deformable derivatives and provide a matrix-based approach to their solution. The given system is first transformed into a comparable classical matrix differential equation using a deformation-adjusted system matrix. This allows us to use popular techniques like the Putzer algorithm & the Cayley-Hamilton theorem to generate explicit solutions. One advantage of this approach is that it doesn’t need eigenvector calculation or diagonalization. To illustrate the method, we look at two scenarios: a radioactive decay-growth scenario and a mortgage payback issue. The findings demonstrate that, for linear constant-coefficient systems, the deformable framework introduces a single parameter \(\theta\) that modifies the effective evolution rate. Although the present analysis is confined to two elementary applications, the numerical experiments suggest that \(\theta\) can be tuned to mimic delayed responses without increasing computational complexity – a feature that may prove useful in domains where fractional models are too heavy.