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The Analytical Analysis of Time-Fractional Fornberg–Whitham Equations

Author

Listed:
  • A. A. Alderremy

    (Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi Arabia)

  • Hassan Khan

    (Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan)

  • Rasool Shah

    (Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan)

  • Shaban Aly

    (Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi Arabia
    Department of Mathematics, Faculty of Science, AL-Azhar University, Assiut 71516, Egypt)

  • Dumitru Baleanu

    (Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
    Institute of Space Sciences, 077125 Magurele, Romania)

Abstract

This article is dealing with the analytical solution of Fornberg–Whitham equations in fractional view of Caputo operator. The effective method among the analytical techniques, natural transform decomposition method, is implemented to handle the solutions of the proposed problems. The approximate analytical solutions of nonlinear numerical problems are determined to confirm the validity of the suggested technique. The solution of the fractional-order problems are investigated for the suggested mathematical models. The solutions-graphs are then plotted to understand the effectiveness of fractional-order mathematical modeling over integer-order modeling. It is observed that the derived solutions have a closed resemblance with the actual solutions. Moreover, using fractional-order modeling various dynamics can be analyzed which can provide sophisticated information about physical phenomena. The simple and straight-forward procedure of the suggested technique is the preferable point and thus can be used to solve other nonlinear fractional problems.

Suggested Citation

  • A. A. Alderremy & Hassan Khan & Rasool Shah & Shaban Aly & Dumitru Baleanu, 2020. "The Analytical Analysis of Time-Fractional Fornberg–Whitham Equations," Mathematics, MDPI, vol. 8(6), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:987-:d:372370
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    References listed on IDEAS

    as
    1. Rasool Shah & Hassan Khan & Poom Kumam & Muhammad Arif, 2019. "An Analytical Technique to Solve the System of Nonlinear Fractional Partial Differential Equations," Mathematics, MDPI, vol. 7(6), pages 1-16, June.
    2. Kalisch, Henrik & Lenells, Jonatan, 2005. "Numerical study of traveling-wave solutions for the Camassa–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 287-298.
    3. Tuan, Nguyen Huy & Baleanu, Dumitru & Thach, Tran Ngoc & O’Regan, Donal & Can, Nguyen Huu, 2020. "Approximate solution for a 2-D fractional differential equation with discrete random noise," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
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