A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation-Reference-Cited by-同舟云学术

A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation

Published:2022-10-06 Issue:0 Volume:0 Page:
ISSN:1565-1339
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Amin Ahmed Z.¹,Lopes António M.²^ORCID,Hashim Ishak¹

Affiliation:

1. Faculty of Science & Technology, Department of Mathematical Sciences , Universiti Kebangsaan , Bangi , Selangor , Malaysia

2. Faculty of Engineering, LAETA/INEGI , University of Porto , Porto , Portugal

Abstract

AbstractA numerical approach based on the shifted Chebyshev–Gauss collocation method is proposed for solving the non-linear variable-order fractional Bagley–Torvik differential equation (VO-FBTE), subject to initial and boundary conditions. The shifted fractional Chebyshev–Gauss collocation points are used as interpolation nodes, and the solution of the VO-FBTE is approximated by a truncated series of the shifted Chebyshev polynomials. The residuals are calculated at the shifted fractional Chebyshev–Gauss quadrature points. The original VO-FBTE is converted into a system of algebraic equations. The accuracy of the proposed scheme is confirmed with a set of numerical examples, and the results are compared with those obtained by other methods.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2021-0395/pdf

Reference50 articles.

1. S. S. Ezz-Eldien, Y. Wang, M. A. Abdelkawy, M. A. Zaky, A. A. Aldraiweesh, and M. J. Tenreiro, “Chebyshev spectral methods for multi-order fractional neutral pantograph equations,” Nonlinear Dynam., vol. 100, no. 4, pp. 3785–3797, 2020. https://doi.org/10.1007/s11071-020-05728-x.

2. R. M. Hafez, M. A. Zaky, and M. A. Abdelkawy, “Jacobi spectral Galerkin method for distributed-order fractional Rayleigh–Stokes problem for a generalized second grade fluid,” Front. Phys., vol. 7, p. 240, 2020. https://doi.org/10.3389/fphy.2019.00240.

3. E. H. Doha, M. A. Abdelkawy, A. Z. M. Amin, and A. M. Lopes, “A space–time spectral approximation for solving nonlinear variable-order fractional sine and Klein–Gordon differential equations,” Comput. Appl. Math., vol. 37, no. 5, pp. 6212–6229, 2018. https://doi.org/10.1007/s40314-018-0695-2.

4. R. M. Hafez and Y. H. Youssri, “Shifted Jacobi collocation scheme for multidimensional time-fractional order telegraph equation,” Iran. J. Numer. Anal. Optim., vol. 10, no. 1, pp. 195–223, 2020.

5. A. S. Hendy, M. A. Zaky, R. M. Hafez, and R. H. De Staelen, “The impact of memory effect on space fractional strong quantum couplers with tunable decay behavior and its numerical simulation,” Sci. Rep., vol. 11, no. 1, pp. 1–15, 2021. https://doi.org/10.1038/s41598-021-89701-7.

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A numerical approach based on the Chebyshev polynomials for tempered time fractional coupled Burger’s equations;Alexandria Engineering Journal;2024-10

2. A Spectral Collocation Method for Solving the Non-Linear Distributed-Order Fractional Bagley–Torvik Differential Equation;Fractal and Fractional;2023-10-26

3. Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation;PLOS ONE;2023-05-26

4. Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations;AIMS Mathematics;2023