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A Matrix Approach by Convolved Fermat Polynomials for Solving the Fractional Burgers’ Equation

Author

Listed:
  • Waleed Mohamed Abd-Elhameed

    (Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt)

  • Omar Mazen Alqubori

    (Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23831, Saudi Arabia)

  • Naher Mohammed A. Alsafri

    (Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23831, Saudi Arabia)

  • Amr Kamel Amin

    (Department of Mathematics, Adham University College, Umm Al-Qura University, Makkah 28653, Saudi Arabia)

  • Ahmed Gamal Atta

    (Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt)

Abstract

This article employs certain polynomials that generalize standard Fermat polynomials, called convolved Fermat polynomials, to numerically solve the fractional Burgers’ equation. New theoretical results of these polynomials are developed and utilized along with the collocation method to find approximate solutions of the fractional Burgers’ equation. The basic idea behind the proposed numerical algorithm is based on establishing the operational matrices of derivatives of both integer and fractional derivatives of the convolved Fermat polynomials that help to convert the equation governed by its underlying conditions into an algebraic system of equations that can be treated numerically. A comprehensive study is performed to analyze the error of the proposed convolved Fermat expansion. Some numerical examples are presented to test our proposed numerical algorithm, and some comparisons are made. The results indicate that the proposed algorithm is applicable and accurate.

Suggested Citation

  • Waleed Mohamed Abd-Elhameed & Omar Mazen Alqubori & Naher Mohammed A. Alsafri & Amr Kamel Amin & Ahmed Gamal Atta, 2025. "A Matrix Approach by Convolved Fermat Polynomials for Solving the Fractional Burgers’ Equation," Mathematics, MDPI, vol. 13(7), pages 1-25, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1135-:d:1624063
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