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A Numerical Method for Delayed Fractional‐Order Differential Equations

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  • Zhen Wang

Abstract

A numerical method for nonlinear fractional‐order differential equations with constant or time‐varying delay is devised. The order here is an arbitrary positive real number, and the differential operator is with the Caputo definition. The general Adams‐Bashforth‐Moulton method combined with the linear interpolation method is employed to approximate the delayed fractional‐order differential equations. Meanwhile, the detailed error analysis for this algorithm is given. In order to compare with the exact analytical solution, a numerical example is provided to illustrate the effectiveness of the proposed method.

Suggested Citation

  • Zhen Wang, 2013. "A Numerical Method for Delayed Fractional‐Order Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:256071
    DOI: 10.1155/2013/256071
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    References listed on IDEAS

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    1. Dadras, Sara & Momeni, Hamid Reza, 2010. "Control of a fractional-order economical system via sliding mode," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2434-2442.
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    Cited by:

    1. V. G. Pimenov & A. S. Hendy, 2015. "Numerical Studies for Fractional Functional Differential Equations with Delay Based on BDF‐Type Shifted Chebyshev Approximations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    2. 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).

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