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Fractional-Order Newton–Raphson Method For Nonlinear Equation With Convergence And Stability Analyses

Author

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  • MUHAMMAD FARMAN

    (Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan†Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon§Near East University, Mathematics Research Center, Near East Boulevard, PC)

  • ALI AKGÃœL

    (��Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon‡Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey§Near East University, Mathematics Research Center, Near East Boulevard, PC)

  • NOORHAN ALSHAIKH

    (�Department of Physics, Faculty of Applied Sciences, Palestine Technical University Kadoorie, Tulkarm, Palestine)

  • MUHAMMAD AZEEM

    (��Department of Mathematics and Statistics, University of Lahore, Lahore 54590, Pakistan)

  • JIHAD ASAD

    (�Department of Physics, Faculty of Applied Sciences, Palestine Technical University Kadoorie, Tulkarm, Palestine**Department of ECE, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India)

Abstract

Fractional-order techniques have many applications in real-life problems nowadays. The utilization of fragmentary math in many parts of science and engineering is wide and somewhat recent. There are various types of subsidiaries that can be valuable in various issues. In this paper, we focus on the effect of this kind of fractional derivative in the search for roots of nonlinear equations and its dependence on the initial estimations. We will check the convergence and stability analyses of the fractional Newton–Raphson (FNR) method for the proposed definitions. We will apply fractional Riemann–Liouville and Caputo-derivatives in the standard Newton root-finding method for different examples and also verify convergence and stability for these problems. Finding a root is very important for nonlinear equations which are used to solve chemical, biological, and engineering problems.

Suggested Citation

  • Muhammad Farman & Ali Akgãœl & Noorhan Alshaikh & Muhammad Azeem & Jihad Asad, 2023. "Fractional-Order Newton–Raphson Method For Nonlinear Equation With Convergence And Stability Analyses," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(10), pages 1-12.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:10:n:s0218348x23400790
    DOI: 10.1142/S0218348X23400790
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