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ARTICLE
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
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.
Citations