Solutions of general fractional-order differential equations by using the spectral Tau method

Date

2021

Authors

Srivastava, H.M.
Gusu, Daba Meshesha
Mohammed, Pshtiwan Othman
Wedajo, Gidisa
Nonlaopon, Kamsing
Hamed, Yasser S.

Journal Title

Journal ISSN

Volume Title

Publisher

Fractal and Fractional

Abstract

Here, in this article, we investigate the solution of a general family of fractional-order differential equations by using the spectral Tau method in the sense of Liouville–Caputo type fractional derivatives with a linear functional argument. We use the Chebyshev polynomials of the second kind to develop a recurrence relation subjected to a certain initial condition. The behavior of the approximate series solutions are tabulated and plotted at different values of the fractional orders υ and α. The method provides an efficient convergent series solution form with easily computable coefficients. The obtained results show that the method is remarkably effective and convenient in finding solutions of fractional-order differential equations.

Description

Keywords

fractional-order differential equations, Caputo fractional-order differential equations, Chebyshev polynomial, spectral Tau method

Citation

Srivastava, H. M., Gusu, D. M., Mohammed, P. O., Wedajo, G., Nonlaopon, K., & Hamed, Y.S. (2021). “Solutions of general fractional-order differential equations by using the spectral Tau method.” Fractal and Fractional, 6(1), 7. https://doi.org/10.3390/fractalfract6010007