Paper Title:

Stability Analysis of Fractional Delay Differential Equations by Chebyshev Polynomial

Periodical Advanced Materials Research (Volume 500)
Main Theme Advances in Materials Processing X
Chapter VI. Analytical and Numerical Methods for Materials Processing
Edited by Chuanzhen Huang, Hongtao Zhu, Jun Wang and Xiaoping Li
Pages 586-590
DOI 10.4028/www.scientific.net/AMR.500.586
Citation Xiang Mei Zhang et al., 2012, Advanced Materials Research, 500, 586
Online since April 2012
Authors Xiang Mei Zhang, Xian Zhou Guo, Anping Xu
Keywords Chebyshev Polynomial, Fractional Derivative, Fractional Differential Equation, Stability
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The paper is devoted to the numerical stability of fractional delay differential equations with non-smooth coefficients using the Chebyshev collocation method. In this paper, based on the Grunwald-Letnikov fractional derivatives, we discuss the approximation of fractional differentiation by the Chebyshev polynomial of the first kind. Then we solve the stability of the fractional delay differential equations. Finally, the stability of the delayed Mathieu equation of fractional order is examined for a set of case studies that contain the complexities of periodic coefficients, delays and discontinuities.

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