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An Effective New Iterative Method to Solve Conformable Cauchy Reaction‐Diffusion Equation via the Shehu Transform

Author

Listed:
  • Shahram Rezapour
  • Muhammad Imran Liaqat
  • Sina Etemad

Abstract

For the first time, we establish a new procedure by using the conformable Shehu transform (CST) and an iteration method for solving fractional‐order Cauchy reaction‐diffusion equations (CRDEs) in the sense of conformable derivative (CD). We call this recommended method the conformable Shehu transform iterative method (CSTIM). To evaluate the efficacy and consistency of CSTIM for conformable partial differential equations (PDEs), the absolute errors of four CRDEs are reviewed graphically and numerically. Furthermore, graphical significances are correspondingly predicted for several values of fractional‐order derivatives. The results and examples establish that our new method is unpretentious, accurate, valid, and capable. CSTIM does not necessarily use He’s polynomials and Adomian polynomials when solving nonlinear problems, so it has a strong advantage over the homotopy analysis and Adomian decomposition methods. The convergence and absolute error analysis of the series solutions is also offered.

Suggested Citation

  • Shahram Rezapour & Muhammad Imran Liaqat & Sina Etemad, 2022. "An Effective New Iterative Method to Solve Conformable Cauchy Reaction‐Diffusion Equation via the Shehu Transform," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4172218
    DOI: 10.1155/2022/4172218
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    References listed on IDEAS

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    1. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. A. Harir & S. Melliani & H. El Harfi & L. S. Chadli, 2020. "Variational Iteration Method and Differential Transformation Method for Solving the SEIR Epidemic Model," International Journal of Differential Equations, Hindawi, vol. 2020, pages 1-7, July.
    3. Adnan Khan & Muhammad Imran Liaqat & Muhammad Younis & Ashraful Alam & Fairouz Tchier, 2021. "Approximate and Exact Solutions to Fractional Order Cauchy Reaction-Diffusion Equations by New Combine Techniques," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, December.
    4. Hashem Najafi & Sina Etemad & Nichaphat Patanarapeelert & Joshua Kiddy K. Asamoah & Shahram Rezapour & Thanin Sitthiwirattham, 2022. "A Study on Dynamics of CD4 + T-Cells under the Effect of HIV-1 Infection Based on a Mathematical Fractal-Fractional Model via the Adams-Bashforth Scheme and Newton Polynomials," Mathematics, MDPI, vol. 10(9), pages 1-32, April.
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    Cited by:

    1. Muhammad Imran Liaqat & Eric Okyere, 2022. "The Fractional Series Solutions for the Conformable Time‐Fractional Swift‐Hohenberg Equation through the Conformable Shehu Daftardar‐Jafari Approach with Comparative Analysis," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    2. 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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