关键词: 移位Chebyshev多项式, 变阶分数阶, 受电弓方程, 收敛性, 稳定性

Abstract: Based on the shift Chebyshev polynomial, a method for solving the numerical solution of the differential equation of variable-order fractional pantograph was constructed. The shift Chebyshev polynomial was used to approximate the derivative of the given order of the unknown function, and then the unknown function and its variable-order fractional derivative were approximated, and the original equation was converted into an algebraic equation system by selecting the configuration point for solving. The error estimation of the method and the theoretical proof of convergence and stability were given. Compared with the existing methods, the numerical simulation of the typical paradigm shows obvious superiority in the calculation accuracy and complexity, which comprehensively shows that the proposed method has certain feasibility and effectiveness.

Key words: displaced Chebyshev polynomial, variable fractional order, pantograph equation, astringency, stability