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Modified Chebyshev wavelet methods for fractional delay-type equations

Author

Listed:
  • Saeed, Umer
  • Rehman, Mujeeb ur
  • Iqbal, Muhammad Asad

Abstract

In this article, we develop the Chebyshev wavelet method for solving the fractional delay differential equations and integro-differential equations. According to the development, we approximate the delay unknown functions by the Chebyshev wavelets series at delay time, which we call the delay Chebyshev wavelet series. We also proposed a technique by combining the method of steps and Chebyshev wavelet method for solving fractional delay differential equations. This technique converts the fractional delay differential equation on a given interval to a fractional non-delay differential equation over that interval, by using the function defined on previous interval, and then apply the Chebyshev wavelet method on the obtained fractional non-delay differential equation to find the solution. Numerical examples will be presented to demonstrate the benefits of computing with these approaches.

Suggested Citation

  • Saeed, Umer & Rehman, Mujeeb ur & Iqbal, Muhammad Asad, 2015. "Modified Chebyshev wavelet methods for fractional delay-type equations," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 431-442.
    • Handle: RePEc:eee:apmaco:v:264:y:2015:i:c:p:431-442
    DOI: 10.1016/j.amc.2015.04.113
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    Cited by:

    1. Chen, Zhong & Gou, QianQian, 2019. "Piecewise Picard iteration method for solving nonlinear fractional differential equation with proportional delays," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 465-478.
    2. Usman, M. & Hamid, M. & Zubair, T. & Haq, R.U. & Wang, W. & Liu, M.B., 2020. "Novel operational matrices-based method for solving fractional-order delay differential equations via shifted Gegenbauer polynomials," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    3. Allahviranloo, Tofigh & Sahihi, Hussein, 2021. "Reproducing kernel method to solve fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    4. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    5. Usman, Muhammad & Hamid, Muhammad & Khan, Zafar Hayat & Haq, Rizwan Ul, 2021. "Neuronal dynamics and electrophysiology fractional model: A modified wavelet approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).

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