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An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations

Author

Listed:
  • Hassan Khan

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

  • Rasool Shah

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

  • Poom Kumam

    (Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Dumitru Baleanu

    (Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey)

  • Muhammad Arif

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

Abstract

In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equations—particularly the fractional-order telegraph equation.

Suggested Citation

  • Hassan Khan & Rasool Shah & Poom Kumam & Dumitru Baleanu & Muhammad Arif, 2019. "An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations," Mathematics, MDPI, vol. 7(5), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:426-:d:230724
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    Citations

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    Cited by:

    1. Alberto Antonini & Valentina Anna Lia Salomoni, 2023. "Modelling Fractional Advection–Diffusion Processes via the Adomian Decomposition," Mathematics, MDPI, vol. 11(12), pages 1-30, June.
    2. Jorge E. Macías-Díaz, 2019. "Numerically Efficient Methods for Variational Fractional Wave Equations: An Explicit Four-Step Scheme," Mathematics, MDPI, vol. 7(11), pages 1-27, November.

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