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A New Numerical Approach for Solving the Fractional Nonlinear Multi-pantograph Delay Differential Equations

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Abstract

The numerical solution of the fractional nonlinear multi-pantograph delay differential equations is investigated by a new class of polynomials. These polynomials are equipped with an unknown auxiliary parameter a, which is obtained by using the collocation and least-squares methods. In this paper, the numerical solution of the fractional nonlinear multi-pantograph delay differential equation is displayed in the truncated series form. The existence and uniqueness of the solution and the error analysis are also investigated in this article. In four examples, the numerical results of the present method have been compared with other methods. For the first time, a-polynomials are used in this article to numerically solve the fractional nonlinear multi-pantograph delay differential equations, and accurate approximations have been displayed.

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Acknowledgements

We thank the anonymous reviewers for helpful comments, which lead to definite improvement in the manuscript.

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The authors have not disclosed any funding.

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Authors and Affiliations

  1. Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran

    J. Hajishafieiha & S. Abbasbandy

  2. Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey

    T. Allahviranloo

Authors
  1. J. Hajishafieiha
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  2. S. Abbasbandy
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  3. T. Allahviranloo
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Correspondence to S. Abbasbandy.

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Hajishafieiha, J., Abbasbandy, S. & Allahviranloo, T. A New Numerical Approach for Solving the Fractional Nonlinear Multi-pantograph Delay Differential Equations. Iran J Sci 47, 825–835 (2023). https://doi.org/10.1007/s40995-023-01457-z

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  • DOI: https://doi.org/10.1007/s40995-023-01457-z

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