Shifted Monic Ultraspherical Approximation for solving some of Fractional Orders Differential Equations
Numerical Analysis
2021-03-23 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2103.10347,
title = {Shifted Monic Ultraspherical Approximation for solving some of Fractional Orders Differential Equations},
author = {M. Abdelhakem and Doha M. R. and A. F. Saadallah and M. El-Kady},
journal= {arXiv preprint arXiv:2103.10347},
year = {2021}
}