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Symmetry
Volume 17
Issue 11
10.3390/sym17111916
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Delannoy Tau-Based Numerical Procedure for the Time-Fractional Cable Model

by
Ahmed Gamal Atta
1,
Mohamed A. Abdelkawy
2,
Naher Mohammed A. Alsafri
3 and
Waleed Mohamed Abd-Elhameed
4,*
1
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt
2
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia
3
Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23831, Saudi Arabia
4
Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
*
Author to whom correspondence should be addressed.
Symmetry 2025, 17(11), 1916; https://doi.org/10.3390/sym17111916 (registering DOI)
Submission received: 27 September 2025 / Revised: 23 October 2025 / Accepted: 6 November 2025 / Published: 8 November 2025
(This article belongs to the Special Issue Symmetry in Fractional Derivatives, Fractional Equations and Fractional Order Systems)
Versions Notes

Abstract

This study uses the spectral tau method to treat the time-fractional cable equation (TFCE). The proposed algorithm uses the shifted Delannoy polynomials, which are non-symmetric orthogonal. The orthogonality property of the non-symmetric shifted Delannoy polynomials and some representations facilitate obtaining accurate spectral approximations for the TFCE. Several numerical examples ensure the efficiency and accuracy of the method. We compare the suggested scheme to other algorithms and benchmark it against existing analytical solutions to demonstrate the high accuracy of our presented algorithm.
Keywords: time-fractional cable problem; tau method; Delannoy polynomials; error analysis time-fractional cable problem; tau method; Delannoy polynomials; error analysis

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MDPI and ACS Style

Atta, A.G.; Abdelkawy, M.A.; Alsafri, N.M.A.; Abd-Elhameed, W.M. Delannoy Tau-Based Numerical Procedure for the Time-Fractional Cable Model. Symmetry 2025, 17, 1916. https://doi.org/10.3390/sym17111916

AMA Style

Atta AG, Abdelkawy MA, Alsafri NMA, Abd-Elhameed WM. Delannoy Tau-Based Numerical Procedure for the Time-Fractional Cable Model. Symmetry. 2025; 17(11):1916. https://doi.org/10.3390/sym17111916

Chicago/Turabian Style

Atta, Ahmed Gamal, Mohamed A. Abdelkawy, Naher Mohammed A. Alsafri, and Waleed Mohamed Abd-Elhameed. 2025. "Delannoy Tau-Based Numerical Procedure for the Time-Fractional Cable Model" Symmetry 17, no. 11: 1916. https://doi.org/10.3390/sym17111916

APA Style

Atta, A. G., Abdelkawy, M. A., Alsafri, N. M. A., & Abd-Elhameed, W. M. (2025). Delannoy Tau-Based Numerical Procedure for the Time-Fractional Cable Model. Symmetry, 17(11), 1916. https://doi.org/10.3390/sym17111916

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