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On Computational Efficient Higher-Order Fractional Scheme For Nonlinear Problems With Engineering Applications

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  • MUDASSIR SHAMS

    (Department of Mathematics, Faculty of Arts and Science, Balikesir University, Balikesir 10145, Turkey†Faculty of Engineering, Free University of Bozen-Bolzano (BZ), Bolzano 39100, Italy‡Department of Mathematics and Statistics, Riphah International University, Islamabad 44000, Pakistan)

  • NASREEN KAUSAR

    (Department of Mathematics, Faculty of Arts and Science, Balikesir University, Balikesir 10145, Turkey)

  • SEIFEDINE KADRY

    (�Department of Computer Science and Mathematics, Lebanese American University, Beirut 1102 2801, Lebanon¶Department of Applied Data Science, Noroff University College, Kristiansand 4608, Norway)

  • JUNGEUN KIM

    (��Department of Computer Engineering, Inha University, Incheon 22212, Republic of Korea)

Abstract

In this study, we offer a novel fractional numerical approach designed to solve nonlinear equations. Based on fractional calculus principles, our technique extends standard numerical methods to account for the fractional-order derivatives found in many real-world occurrences. Analysis of convergence reveals that the order of convergence of the suggested family of approaches is 4β + 1 and 8β + 4, respectively. We assess the efficacy and convergence qualities of our proposed approach in solving nonlinear equations in various settings using rigorous analysis and numerical experiments. Fractal analysis of the suggested numerical methods for solving nonlinear equations indicates improved convergence behavior and stability than classical methods in the literature.

Suggested Citation

  • Mudassir Shams & Nasreen Kausar & Seifedine Kadry & Jungeun Kim, 2025. "On Computational Efficient Higher-Order Fractional Scheme For Nonlinear Problems With Engineering Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(06), pages 1-16.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:06:n:s0218348x25401267
    DOI: 10.1142/S0218348X25401267
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