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Analytical Solutions to Two‐Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method

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  • Alemayehu Tamirie Deresse

Abstract

The conformable fractional triple Laplace transform approach, in conjunction with the new Iterative method, is used to examine the exact analytical solutions of the (2 + 1)‐dimensional nonlinear conformable fractional Telegraph equation. All the fractional derivatives are in a conformable sense. Some basic properties and theorems for conformable triple Laplace transform are presented and proved. The linear part of the considered problem is solved using the conformable fractional triple Laplace transform method, while the noise terms of the nonlinear part of the equation are removed using the novel Iterative method’s consecutive iteration procedure, and a single iteration yields the exact solution. As a result, the proposed method has the benefit of giving an exact solution that can be applied analytically to the presented issues. To confirm the performance, correctness, and efficiency of the provided technique, two test modeling problems from mathematical physics, nonlinear conformable fractional Telegraph equations, are used. According to the findings, the proposed method is being used to solve additional forms of nonlinear fractional partial differential equation systems. Moreover, the conformable fractional triple Laplace transform iterative method has a small computational size as compared to other methods.

Suggested Citation

  • Alemayehu Tamirie Deresse, 2022. "Analytical Solutions to Two‐Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:4552179
    DOI: 10.1155/2022/4552179
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    References listed on IDEAS

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    1. Sachin Bhalekar & Varsha Daftardar-Gejji, 2011. "Convergence of the New Iterative Method," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-10, November.
    2. Amjad E. Hamza & Mohamed Z. Mohamed & Eltaib M. Abd Elmohmoud & M. Magzoub, 2021. "Conformable Sumudu Transform of Space‐Time Fractional Telegraph Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2021(1).
    3. Alemayehu Tamirie Deresse & Yesuf Obsie Mussa & Ademe Kebede Gizaw, 2021. "Solutions of Two-Dimensional Nonlinear Sine-Gordon Equation via Triple Laplace Transform Coupled with Iterative Method," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-15, October.
    4. Amjad E. Hamza & Mohamed Z. Mohamed & Eltaib M. Abd Elmohmoud & M. Magzoub, 2021. "Conformable Sumudu Transform of Space-Time Fractional Telegraph Equation," Abstract and Applied Analysis, Hindawi, vol. 2021, pages 1-6, April.
    5. Shailesh A. Bhanotar & Mohammed K. A. Kaabar, 2021. "Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method," International Journal of Differential Equations, Hindawi, vol. 2021, pages 1-18, August.
    6. Akgül, Esra Karatas & Akgül, Ali & Yavuz, Mehmet, 2021. "New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. Alemayehu Tamirie Deresse & Yesuf Obsie Mussa & Ademe Kebede Gizaw, 2021. "Solutions of Two‐Dimensional Nonlinear Sine‐Gordon Equation via Triple Laplace Transform Coupled with Iterative Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2021(1).
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    1. Asfaw Tsegaye Moltot & Alemayehu Tamirie Deresse, 2022. "Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).

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