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Explicit Shifted Second-kind Chebyshev Spectral Treatment for Fractional Riccati Differential Equation

W. M. Abd-Elhameed1,2,*, Y. H. Youssri2
1 Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia.
2 Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt.
∗ Corresponding Author: W. M. Abd-Elhameed. Email: .

Computer Modeling in Engineering & Sciences 2019, 121(3), 1029-1049. https://doi.org/10.32604/cmes.2019.08378

Abstract

This paper is confined to analyzing and implementing new spectral solutions of the fractional Riccati differential equation based on the application of the spectral tau method. A new explicit formula for approximating the fractional derivatives of shifted Chebyshev polynomials of the second kind in terms of their original polynomials is established. This formula is expressed in terms of a certain terminating hypergeometric function of the type 4F3(1). This hypergeometric function is reduced in case of the integer case into a certain terminating hypergeometric function of the type 3F2(1) which can be summed with the aid of Watson’s identity. Six illustrative examples are presented to ensure the applicability and accuracy of the proposed algorithm.

Keywords

Chebyshev polynomials of the second kind, spectral methods, linearization formula, hypergeometric functions.

Cite This Article

Abd-Elhameed, W. M., Youssri, Y. H. (2019). Explicit Shifted Second-kind Chebyshev Spectral Treatment for Fractional Riccati Differential Equation. CMES-Computer Modeling in Engineering & Sciences, 121(3), 1029–1049.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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