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Numerical Approach for Solving the Fractional Pantograph Delay Differential Equations

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  • Jalal Hajishafieiha
  • Saeid Abbasbandy

Abstract

A new class of polynomials investigates the numerical solution of the fractional pantograph delay ordinary differential equations. These polynomials are equipped with an auxiliary unknown parameter a, which is obtained using the collocation and least‐squares methods. In this study, the numerical solution of the fractional pantograph delay differential equation is displayed in the truncated series form. The upper bound of the solution as well as the error analysis and the rate of convergence theorem are also investigated in this study. In five examples, the numerical results of the present method have been compared with other methods. For the first time, a‐polynomials are used in this study to numerically solve delay equations, and accurate approximations have been displayed.

Suggested Citation

  • Jalal Hajishafieiha & Saeid Abbasbandy, 2022. "Numerical Approach for Solving the Fractional Pantograph Delay Differential Equations," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:4134892
    DOI: 10.1155/2022/4134892
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    References listed on IDEAS

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    1. 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).
    2. Saadia Masood & Muhammad Naeem & Roman Ullah & Saima Mustafa & Abdul Bariq & Fathalla A. Rihan, 2022. "Analysis of the Fractional-Order Delay Differential Equations by the Numerical Method," Complexity, Hindawi, vol. 2022, pages 1-14, March.
    3. Bellen, Alfredo & Zennaro, Marino, 2013. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780199671373.
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