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A Novel Solution Approach for Time-Fractional Hyperbolic Telegraph Differential Equation with Caputo Time Differentiation

Author

Listed:
  • Mohammad Alaroud

    (Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, Jordan)

  • Abedel-Karrem Alomari

    (Department of Mathematics, Faculty of Science, Yarmouk University, Irbid 22163, Jordan)

  • Nedal Tahat

    (Department of Mathematics, Faculty of Science, The Hashemite University, Zarqa 13133, Jordan)

  • Shrideh Al-Omari

    (Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan)

  • Anuar Ishak

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

Abstract

In the current analysis, a specific efficient and applicable novel solution approach, based on a fractional power series technique and Laplace transform operator, is considered to predict certain accurate approximate solutions (ASs) for a time-fractional hyperbolic telegraph equation by aid of time-fractional derivatives in a Caputo sense. The solutions are obtained in a fractional Maclurian series formula by solving the original problem in the Laplace space aided by a limit concept having fewer small iterations than the classical fractional power series technique. To confirm applicability and feasibility of the proposed approach, three appropriate initial value problems are considered. Consequently, some simulations of gained outcomes are numerically and graphically implemented to support the effect of the fractional-order parameter on the geometric behavior of the obtained solutions. In addition, graphical representations are also fulfilled to verify the convergence analysis of the fractional series solutions of the classical solution. The proposed technique is therefore proposed to be a straightforward, accurate and powerful approach for handling varied time-fractional models in various physical phenomena.

Suggested Citation

  • Mohammad Alaroud & Abedel-Karrem Alomari & Nedal Tahat & Shrideh Al-Omari & Anuar Ishak, 2023. "A Novel Solution Approach for Time-Fractional Hyperbolic Telegraph Differential Equation with Caputo Time Differentiation," Mathematics, MDPI, vol. 11(9), pages 1-19, May.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2181-:d:1140144
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    References listed on IDEAS

    as
    1. Singh, Jagdev & Kumar, Devendra & Baleanu, Dumitru & Rathore, Sushila, 2018. "An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 12-24.
    2. Anas Arafa & Ghada Elmahdy, 2018. "Application of Residual Power Series Method to Fractional Coupled Physical Equations Arising in Fluids Flow," International Journal of Differential Equations, Hindawi, vol. 2018, pages 1-10, July.
    3. Shaher Momani & Asad Freihat & Mohammed AL-Smadi, 2014. "Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, June.
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