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A Hybrid Interpolation Method for Fractional PDEs and Its Applications to Fractional Diffusion and Buckmaster Equations

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  • Ihtisham Ul Haq
  • Nigar Ali
  • Shabir Ahmad
  • Tayyaba Akram
  • Ibrahim Mahariq

Abstract

This study presents a novel numerical method to solve PDEs with the fractional Caputo operator. In this method, we apply the Newton interpolation numerical scheme in Laplace space, and then, the solution is returned to real space through the inverse Laplace transform. The Newton polynomial provides good results as compared to the Lagrangian polynomial, which is used to construct the Adams–Bashforth method. This procedure is used to solve fractional Buckmaster and diffusion equations. Finally, a few numerical simulations are presented, ensuring that this strategy is highly stable and quickly converges to an exact solution.

Suggested Citation

  • Ihtisham Ul Haq & Nigar Ali & Shabir Ahmad & Tayyaba Akram & Ibrahim Mahariq, 2022. "A Hybrid Interpolation Method for Fractional PDEs and Its Applications to Fractional Diffusion and Buckmaster Equations," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-12, June.
    • Handle: RePEc:hin:jnlmpe:2517602
    DOI: 10.1155/2022/2517602
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    Cited by:

    1. Xu, Changjin & Liu, Zixin & Pang, Yicheng & Akgül, Ali & Baleanu, Dumitru, 2022. "Dynamics of HIV-TB coinfection model using classical and Caputo piecewise operator: A dynamic approach with real data from South-East Asia, European and American regions," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Mahmood, Tariq & Al-Duais, Fuad S. & Sun, Mei, 2022. "Dynamics of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) involving fractional derivative with Mittag-Leffler kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).

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