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Analysis of the Fractional‐Order Delay Differential Equations by the Numerical Method

Author

Listed:
  • Saadia Masood
  • Muhammad Naeem
  • Roman Ullah
  • Saima Mustafa
  • Abdul Bariq

Abstract

In this study, we implemented a new numerical method known as the Chebyshev Pseudospectral method for solving nonlinear delay differential equations having fractional order. The fractional derivative is defined in Caputo manner. The proposed method is simple, effective, and straightforward as compared to other numerical techniques. To check the validity and accuracy of the proposed method, some illustrative examples are solved by using the present scenario. The obtained results have confirmed the greater accuracy than the modified Laguerre wavelet method, the Chebyshev wavelet method, and the modified wavelet‐based algorithm. Moreover, based on the novelty and scientific importance, the present method can be extended to solve other nonlinear fractional‐order delay differential equations.

Suggested Citation

  • Saadia Masood & Muhammad Naeem & Roman Ullah & Saima Mustafa & Abdul Bariq, 2022. "Analysis of the Fractional‐Order Delay Differential Equations by the Numerical Method," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:3218213
    DOI: 10.1155/2022/3218213
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    References listed on IDEAS

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    1. Sachin Bhalekar & Varsha Daftardar-Gejji, 2011. "Antisynchronization of Nonidentical Fractional-Order Chaotic Systems Using Active Control," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-13, September.
    2. Zhen Wang, 2013. "A Numerical Method for Delayed Fractional-Order Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, May.
    3. Zhen Wang, 2013. "A Numerical Method for Delayed Fractional‐Order Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Noufe H. Aljahdaly & Ravi P. Agarwal & Rasool Shah & Thongchai Botmart, 2021. "Analysis of the Time Fractional-Order Coupled Burgers Equations with Non-Singular Kernel Operators," Mathematics, MDPI, vol. 9(18), pages 1-24, September.
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    Cited by:

    1. Jalal Hajishafieiha & Saeid Abbasbandy, 2022. "Numerical Approach for Solving the Fractional Pantograph Delay Differential Equations," Complexity, John Wiley & Sons, vol. 2022(1).

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