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A computational algorithm for the numerical solution of fractional order delay differential equations

Author

Listed:
  • Amin, Rohul
  • Shah, Kamal
  • Asif, Muhammad
  • Khan, Imran

Abstract

In this paper, a collocation technique based on Haar wavelet is developed for the solution of delay fractional order differential equations (FODEs). The developed technique is applied to both nonlinear and linear delay FODEs. The Haar technique reduces the given equations to a system of nonlinear and linear algebraic equations. The derived nonlinear system is solved by Broyden’s technique while the linear system is solved by Gauss elimination technique. Some examples are taken from literature for checking the validation and convergence of the Haar collocation technique. The comparison of approximate and exact solution are given in figures. The mean square root and maximum absolute errors for distant number of grid points are calculated. The results show that Haar wavelet collocation technique (HWCT) is easy and efficient for solving delay type FODEs. Fractional derivative is described in the Caputo sense throughout the paper.

Suggested Citation

  • Amin, Rohul & Shah, Kamal & Asif, Muhammad & Khan, Imran, 2021. "A computational algorithm for the numerical solution of fractional order delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    • Handle: RePEc:eee:apmaco:v:402:y:2021:i:c:s009630032030816x
    DOI: 10.1016/j.amc.2020.125863
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    References listed on IDEAS

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    1. Hsiao, Chun-Hui, 1997. "State analysis of linear time delayed systems via Haar wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(5), pages 457-470.
    2. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    3. Nazir, Shah & Shahzad, Sara & Wirza, Rahmita & Amin, Rohul & Ahsan, Muhammad & Mukhtar, Neelam & García-Magariño, Iván & Lloret, Jaime, 2019. "Birthmark based identification of software piracy using Haar wavelet," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 144-154.
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    Cited by:

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    2. Samir A. El-Tantawy & Rasool Shah & Albandari W. Alrowaily & Nehad Ali Shah & Jae Dong Chung & Sherif. M. E. Ismaeel, 2023. "A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System," Mathematics, MDPI, vol. 11(7), pages 1-15, April.
    3. Haifa Bin Jebreen & Ioannis Dassios, 2024. "The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations," Mathematics, MDPI, vol. 12(21), pages 1-15, October.
    4. Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Guirao, Juan L.G. & Saeed, Tareq, 2021. "Meyer wavelet neural networks to solve a novel design of fractional order pantograph Lane-Emden differential model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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