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Generalized Lucas Polynomial Sequence Treatment of Fractional Pantograph Differential Equation

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Abstract

This paper deals with the implementation and presentation of numerical solutions of fractional pantograph differential equations (FPDEs) using generalized Lucas polynomials (GLPs). The derivation of our proposed algorithms is built on introducing an operational matrix of derivatives (OMDs) of the GLPs and after that employing it to convert the problem into an algebraic system of equations whose solution can be found through some suitable algorithms such as Gauss elimination and Newton–Raphson methods. Finally, by providing various illustrative examples, including comparisons with the results obtained by some other existing literature methods, the efficiency and applicability of our proposed algorithms are demonstrated.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt

    Y. H. Youssri & W. M. Abd-Elhameed

  2. Department of Mathematics, Faculty of Science, Helwan University, Cairo, 11795, Egypt

    A. S. Mohamed & S. M. Sayed

Authors
  1. Y. H. Youssri
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  2. W. M. Abd-Elhameed
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  3. A. S. Mohamed
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  4. S. M. Sayed
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Correspondence to Y. H. Youssri.

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Youssri, Y.H., Abd-Elhameed, W.M., Mohamed, A.S. et al. Generalized Lucas Polynomial Sequence Treatment of Fractional Pantograph Differential Equation. Int. J. Appl. Comput. Math 7, 27 (2021). https://doi.org/10.1007/s40819-021-00958-y

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