Shifted Monic Ultraspherical Approximation for solving some of Fractional Orders Differential Equations

M. Abdelhakem; Doha M. R.; A. F. Saadallah; M. El-Kady

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arXiv · 2103.10347

Shifted Monic Ultraspherical Approximation for solving some of Fractional Orders Differential Equations

M. Abdelhakem·Doha M. R.·A. F. Saadallah·M. El-Kady

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Abstract

The purpose of this paper is to show and explain a new formula that indicates with finality the derivatives of Shifted Monic Ultraspherical polynomials (SMUPs) of any degree and for any fractional-order using the shifted Monic Ultraspherical polynomials themselves. We also create a direct method solution for the linear or nonlinear multi-order fractional differential equations (FDEs) with constant coefficients involving a spectral Galerkin method. The spatial approximation with its fractional order derivatives (described in the Caputo sense) are built using shifted Monic Ultraspherical polynomials.

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M. Abdelhakem, Doha M. R., A. F. Saadallah, M. El-Kady. 2021-03-18. Shifted Monic Ultraspherical Approximation for solving some of Fractional Orders Differential Equations. https://arxiv.org/abs/2103.10347

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