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Related Experiment Video

Updated: May 15, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
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Matrix-based solution methods for deformable derivative systems: applications to growth-decay and mortgage models.

Komal Priya1, Mohammad Ayman-Mursaleen2, Amit Ujlayan1

  • 1Department of Applied Mathematics, Gautam Buddha University, Greater Noida, Uttar Pradesh, 201312, India.

Scientific Reports
|May 13, 2026
PubMed
Summary

This study introduces a matrix-based method for solving linear systems with deformable derivatives. A parameter θ modifies the evolution rate, potentially mimicking delayed responses efficiently.

Keywords:
Cayley-Hamilton theoremDecay-growth modelsDeformable derivativesLinear systemsMatrix methodsMortgage repaymentPutzer algorithm

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Area of Science:

  • Mathematics
  • Differential Equations
  • Numerical Analysis

Background:

  • Linear systems with derivatives are fundamental in modeling dynamic processes.
  • Traditional methods for solving such systems can be computationally intensive, especially those involving diagonalization.
  • Deformable derivatives offer a novel framework for analyzing system dynamics.

Purpose of the Study:

  • To develop a matrix-based approach for solving linear systems with deformable derivatives.
  • To demonstrate the utility of this method through practical examples.
  • To explore the role of a new parameter in system evolution.

Main Methods:

  • Transformation of the deformable derivative system into a classical matrix differential equation.
  • Utilizing the Putzer algorithm and Cayley-Hamilton theorem for explicit solutions.
  • Introducing a deformation-adjusted system matrix.

Main Results:

  • The proposed method avoids eigenvector calculations and diagonalization.
  • A single parameter θ was identified, which modifies the effective evolution rate of linear constant-coefficient systems.
  • The parameter θ can tune system response to mimic delays without significant computational overhead.

Conclusions:

  • The matrix-based approach provides an efficient alternative for solving linear systems with deformable derivatives.
  • The deformable framework with parameter θ offers a computationally light method for simulating delayed responses.
  • This method shows promise for applications where fractional models are computationally prohibitive.