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An Efficient Technique of Fractional-Order Physical Models Involving ρ -Laplace Transform

Author

Listed:
  • Nehad Ali Shah

    (Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea)

  • Ioannis Dassios

    (AMPSAS, University College Dublin, D04 V1W8 Dublin, Ireland)

  • Essam R. El-Zahar

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, P.O. Box 83, Al-Kharj 11942, Saudi Arabia
    Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt)

  • Jae Dong Chung

    (Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea)

Abstract

In this article, the ρ -Laplace transform is paired with a new iterative method to create a new hybrid methodology known as the new iterative transform method (NITM). This method is applied to analyse fractional-order third-order dispersive partial differential equations. The suggested technique procedure is straightforward and appealing, and it may be used to solve non-linear fractional-order partial differential equations effectively. The Caputo operator is used to express the fractional derivatives. Four numerical problems involving fractional-order third-order dispersive partial differential equations are presented with their analytical solutions. The graphs determined that their findings are in excellent agreement with the precise answers to the targeted issues. The solution to the problems at various fractional orders is achieved and found to be correct while comparing the exact solutions at integer-order problems. Although both problems are the non-linear fractional system of partial differential equations, the present technique provides its solution sophisticatedly. Including both integer and fractional order issues, solution graphs are carefully drawn. The fact that the issues’ physical dynamics completely support the solutions at both fractional and integer orders is significant. Moreover, despite using very few terms of the series solution attained by the present technique, higher accuracy is observed. In light of the various and authentic features, it can be customized to solve different fractional-order non-linear systems in nature.

Suggested Citation

  • Nehad Ali Shah & Ioannis Dassios & Essam R. El-Zahar & Jae Dong Chung, 2022. "An Efficient Technique of Fractional-Order Physical Models Involving ρ -Laplace Transform," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:816-:d:764018
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    References listed on IDEAS

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    3. Hajipour, Mojtaba & Jajarmi, Amin & Malek, Alaeddin & Baleanu, Dumitru, 2018. "Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 146-158.
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    5. M. A. Abdou & Saud Owyed & S. Saha Ray & Yu-Ming Chu & Mustafa Inc & Loubna Ouahid, 2020. "Fractal Ion Acoustic Waves of the Space-Time Fractional Three Dimensional KP Equation," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-7, October.
    6. Yang, Xiao-Jun & Tenreiro Machado, J.A. & Srivastava, H.M., 2016. "A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 143-151.
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