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Generalized Lucas polynomial sequence approach for fractional differential equations

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Abstract

This article is interested in presenting and implementing two new numerical algorithms for solving multi-term fractional differential equations. The idea behind the proposed algorithms is based on establishing a novel operational matrix of fractional-order differentiation of generalized Lucas polynomials in the Caputo sense. This operational matrix serves as a powerful tool for obtaining the desired numerical solutions. The resulting solutions are spectral, and they are built on utilizing tau and collocation methods. A new treatment of convergence and error analysis of the suggested generalized Lucas expansion is presented. The presented numerical results demonstrate the efficiency, applicability and high accuracy of the proposed algorithms.

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Acknowledgements

The authors would like to thank the three anonymous referees for critically reading the manuscript and also for their constructive comments, which helped substantially to improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, 21589, Saudi Arabia

    W. M. Abd-Elhameed

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

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

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  1. W. M. Abd-Elhameed
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  2. Y. H. Youssri
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Correspondence to W. M. Abd-Elhameed.

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Abd-Elhameed, W.M., Youssri, Y.H. Generalized Lucas polynomial sequence approach for fractional differential equations. Nonlinear Dyn 89, 1341–1355 (2017). https://doi.org/10.1007/s11071-017-3519-9

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