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Analysis of RL electric circuits modeled by fractional Riccati IVP via Jacobi-Broyden Newton algorithm

Author

Listed:
  • Mahmoud Abd El-Hady
  • Mohamed El-Gamel
  • Homan Emadifar
  • Atallah El-shenawy

Abstract

This paper focuses on modeling Resistor-Inductor (RL) electric circuits using a fractional Riccati initial value problem (IVP) framework. Conventional models frequently neglect the complex dynamics and memory effects intrinsic to actual RL circuits. This study aims to develop a more precise representation using a fractional-order Riccati model. We present a Jacobi collocation method combined with the Jacobi-Newton algorithm to address the fractional Riccati initial value problem. This numerical method utilizes the characteristics of Jacobi polynomials to accurately approximate solutions to the nonlinear fractional differential equation. We obtain the requisite Jacobi operational matrices for the discretization of fractional derivatives, therefore converting the initial value problem into a system of algebraic equations. The convergence and precision of the proposed algorithm are meticulously evaluated by error and residual analysis. The theoretical findings demonstrate that the method attains high-order convergence rates, dependent on suitable criteria related to the fractional-order parameters and the solution’s smoothness. This study not only improves comprehension of RL circuit dynamics but also offers a solid numerical foundation for addressing intricate fractional differential equations.

Suggested Citation

  • Mahmoud Abd El-Hady & Mohamed El-Gamel & Homan Emadifar & Atallah El-shenawy, 2025. "Analysis of RL electric circuits modeled by fractional Riccati IVP via Jacobi-Broyden Newton algorithm," PLOS ONE, Public Library of Science, vol. 20(1), pages 1-28, January.
    • Handle: RePEc:plo:pone00:0316348
    DOI: 10.1371/journal.pone.0316348
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    References listed on IDEAS

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    1. Abdelkawy, M.A. & Lopes, António M. & Babatin, Mohammed M., 2020. "Shifted fractional Jacobi collocation method for solving fractional functional differential equations of variable order," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Odibat, Zaid & Momani, Shaher, 2008. "Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 167-174.
    3. Singh, Harendra, 2018. "Approximate solution of fractional vibration equation using Jacobi polynomials," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 85-100.
    4. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
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    1. Hany M. Ahmed & Mohammad Izadi & Carlo Cattani, 2025. "A Spectral Approach to Variable-Order Fractional Differential Equations: Improved Operational Matrices for Fractional Jacobi Functions," Mathematics, MDPI, vol. 13(16), pages 1-18, August.

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