Stability Analysis of Fractional Delay Differential Equations by Lagrange Polynomial

Abstract:

The paper deals with the numerical stability analysis of fractional delay differential equations with non-smooth coefficients using the Lagrange collocation method. In this paper, based on the Grunwald-Letnikov fractional derivatives, we discuss the approximation of fractional differentiation by the Lagrange polynomial. Then we study the numerical stability of the fractional delay differential equations. Finally, the stability of the delayed Mathieu equation of fractional order is studied and examined by Lagrange collocation method.

• Periodical: Advanced Materials Research (Volume 500)
• Pages: 591-595
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.500.591
• Online since: April 2012
• Authors: Xiang Mei Zhang, An Ping Xu, Xian Zhou Guo
• Keywords: Fractional Calculus, Fractional Differential Equation, Lagrange Polynomial, Stability

References

[1] Miller, K.S. and B. Ross, An Introduction to the Fractional Calculus and Fractional Equations, (1993) (Wiley, New York).

[2] Carl Boor, Amos Ron. On multivariate polynomial interpolation. Constructive Approximation, (1990), 6(3).

[3] J. Berrut, L.N. Trefethen. Barycentric Lagrange interpolation. SIAM Rev (2004), 46(3), 501-517.

DOI: 10.1137/s0036144502417715

[4] K . Jilien, M . Watson, Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods, J Comput Phys. (2009), 228(5), 1480-1503.

DOI: 10.1016/j.jcp.2008.10.043

[5] Zhou Heng, Wang Renhong, Lagrange Interpolation on a Sphere. Northeastern Mathematical Journal, (2006), 02.