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An Efficient Numerical Approach for Solving Systems of Fractional Problems and Their Applications in Science

Author

Listed:
  • Sondos M. Syam

    (Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia)

  • Z. Siri

    (Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia)

  • Sami H. Altoum

    (Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Al Qunfudhah 24382, Saudi Arabia
    Department of Mathematics, Academy of Engineering and Medical Sciences, Khartoum 11115, Sudan)

  • R. Md. Kasmani

    (Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia)

Abstract

In this article, we present a new numerical approach for solving a class of systems of fractional initial value problems based on the operational matrix method. We derive the method and provide a convergence analysis. To reduce computational cost, we transform the algebraic problem produced by this approach into a set of 2 × 2 nonlinear equations, instead of solving a system of 2 m × 2 m equations. We apply our approach to three main applications in science: optimal control problems, Riccati equations, and clock reactions. We compare our results with those of other researchers, considering computational time, cost, and absolute errors. Additionally, we validate our numerical method by comparing our results with the integer model when the fractional order approaches one. We present numerous figures and tables to illustrate our findings. The results demonstrate the effectiveness of the proposed approach.

Suggested Citation

  • Sondos M. Syam & Z. Siri & Sami H. Altoum & R. Md. Kasmani, 2023. "An Efficient Numerical Approach for Solving Systems of Fractional Problems and Their Applications in Science," Mathematics, MDPI, vol. 11(14), pages 1-21, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3132-:d:1195070
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    References listed on IDEAS

    as
    1. Syam, Muhammed I. & Sharadga, Mwaffag & Hashim, I., 2021. "A numerical method for solving fractional delay differential equations based on the operational matrix method," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Amin, Rohul & Ahmad, Hijaz & Shah, Kamal & Bilal Hafeez, M. & Sumelka, W., 2021. "Theoretical and computational analysis of nonlinear fractional integro-differential equations via collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
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    Cited by:

    1. Gui-Lai Zhang & Chao Liu, 2024. "Two Schemes of Impulsive Runge–Kutta Methods for Linear Differential Equations with Delayed Impulses," Mathematics, MDPI, vol. 12(13), pages 1-17, July.
    2. Md. Habibur Rahman & Muhammad I. Bhatti & Nicholas Dimakis, 2023. "Employing a Fractional Basis Set to Solve Nonlinear Multidimensional Fractional Differential Equations," Mathematics, MDPI, vol. 11(22), pages 1-15, November.

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