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Effective Method for Solving Different Types of Nonlinear Fractional Burgers’ Equations

Author

Listed:
  • Safyan Mukhtar

    (Preparatory Year Deanship, King Faisal University, Hofuf 31982, Al-Hasa, Saudi Arabia)

  • Salah Abuasad

    (Preparatory Year Deanship, King Faisal University, Hofuf 31982, Al-Hasa, Saudi Arabia)

  • Ishak Hashim

    (Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, UKM Bangi 43600, Selangor, Malaysia)

  • Samsul Ariffin Abdul Karim

    (Fundamental and Applied Sciences Department and Center for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, Seri Iskandar 32610, Perak DR, Malaysia)

Abstract

In this study, a relatively new method to solve partial differential equations (PDEs) called the fractional reduced differential transform method (FRDTM) is used. The implementation of the method is based on an iterative scheme in series form. We test the proposed method to solve nonlinear fractional Burgers equations in one, two coupled, and three dimensions. To show the efficiency and accuracy of this method, we compare the results with the exact solutions, as well as some established methods. Approximate solutions for different values of fractional derivatives together with exact solutions and absolute errors are represented graphically in two and three dimensions. From all numerical results, we can conclude the efficiency of the proposed method for solving different types of nonlinear fractional partial differential equations over existing methods.

Suggested Citation

  • Safyan Mukhtar & Salah Abuasad & Ishak Hashim & Samsul Ariffin Abdul Karim, 2020. "Effective Method for Solving Different Types of Nonlinear Fractional Burgers’ Equations," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:729-:d:354330
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    References listed on IDEAS

    as
    1. Momani, Shaher, 2006. "Non-perturbative analytical solutions of the space- and time-fractional Burgers equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 930-937.
    2. Salah Abuasad & Ishak Hashim & Samsul Ariffin Abdul Karim, 2019. "Modified Fractional Reduced Differential Transform Method for the Solution of Multiterm Time-Fractional Diffusion Equations," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-14, May.
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