Tau algorithm for fractional delay differential equations utilizing seventh-kind Chebyshev polynomials

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Abd Elhameed Waleed Mohamed; Youssri Youssri Hassan; Atta Ahmed Gamal

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Journal Paper

Paper Information

Journal: Journal of Mathematical Modeling Year:2024 | Volume:12 | Issue:2 Page(s): 277-299

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Information Journal Paper

Title

Tau algorithm for fractional delay differential equations utilizing seventh-kind Chebyshev polynomials

Author(s)

Abd Elhameed Waleed Mohamed | Youssri Youssri Hassan | Atta Ahmed Gamal | Issue Writer Certificate

Keywords

Chebyshev polynomials

trigonometric representation

spectral tau method

fractional differential equations

convergence analysis

Abstract

Herein, we present an algorithm for handling fractional delay differential equations (FDDEs). Chebyshev polynomials (CPs) class of the seventh kind is a subclass of the generalized Gegenbauer (ultraspherical) polynomials. The members of this class make up the basis functions in this paper. Our suggested numerical algorithm is derived using new theoretical findings about these polynomials and their shifted counterparts. We will use the Tau method to convert the FDDE with the governing conditions into a linear algebraic system, which can then be solved numerically using a suitable procedure. We will give a detailed discussion of the convergence and error analysis of the shifted Chebyshev expansion. Lastly, some numerical examples are provided to verify the precision and applicability of the proposed strategy.

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