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On Efficient Fractional Caputo-Type Simultaneous Scheme For Finding All Roots Of Polynomial Equations With Biomedical Engineering Applications

Author

Listed:
  • MUDASSIR SHAMS

    (Department of Mathematics and Statistics, Riphah International University, Islamabad 44000, Pakistan)

  • NASREEN KAUSAR

    (��Department of Mathematics, Yildiz Technical University, Faculty of Arts and Science, Esenler, 34220 Istanbul, Turkey)

  • CUAUHTÉMOC SAMANIEGO

    (��American University of the Middle East, Department of Mathematics and Statistics, Egaila 54200, Kuwait)

  • PRAVEEN AGARWAL

    (�Department of Mathematics, Anand International, College of Engineering Jaipur, Rajasthan, India¶Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, Russian Federation∥Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE)

  • SHAMS FORRUQUE AHMED

    (*Science and Math Program, Asian University for Women, Chattogram 4000, Bangladesh)

  • SHAHER MOMANI

    (��†Department of Mathematics, The University of Jordan, Amman 11942, Jordan)

Abstract

This research paper introduces a novel fractional Caputo-type simultaneous method for finding all simple and multiple roots of polynomial equations. Without any additional polynomial and derivative evaluations using suitable correction, the order of convergence of the basic Aberth–Ehrlich simultaneous method has been increased from three to α + 3. In terms of accuracy, residual graph, computational efficiency and computation CPU time, the newly proposed families of simultaneous methods outperforms existing methods in numerical applications.

Suggested Citation

  • Mudassir Shams & Nasreen Kausar & Cuauhtã‰Moc Samaniego & Praveen Agarwal & Shams Forruque Ahmed & Shaher Momani, 2023. "On Efficient Fractional Caputo-Type Simultaneous Scheme For Finding All Roots Of Polynomial Equations With Biomedical Engineering Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-15.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:04:n:s0218348x23400753
    DOI: 10.1142/S0218348X23400753
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    Citations

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    Cited by:

    1. Mudassir Shams, 2024. "On a Stable Multiplicative Calculus-Based Hybrid Parallel Scheme for Nonlinear Equations," Mathematics, MDPI, vol. 12(22), pages 1-29, November.
    2. Mudassir Shams & Bruno Carpentieri, 2023. "On Highly Efficient Fractional Numerical Method for Solving Nonlinear Engineering Models," Mathematics, MDPI, vol. 11(24), pages 1-30, December.
    3. Mudassir Shams & Nasreen Kausar & Ioana Alexandra Șomîtcă, 2024. "Efficient Multiplicative Calculus-Based Iterative Scheme for Nonlinear Engineering Applications," Mathematics, MDPI, vol. 12(22), pages 1-26, November.

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