Stability Analysis of Fractional Delay Differential Equations by Chebyshev Polynomial
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.
Chuanzhen Huang, Hongtao Zhu, Jun Wang and Xiaoping Li
X. M. Zhang et al., "Stability Analysis of Fractional Delay Differential Equations by Chebyshev Polynomial", Advanced Materials Research, Vol. 500, pp. 586-590, 2012