Computing Numerical Solutions of Delayed Fractional Differential Equations With Time Varying Coefficients

Fractional differential equations with time varying coefficients and delay are encountered in the analysis of models of metal cutting processes such as milling and drilling with viscoelastic damping elements. Viscoelastic damping is modeled as a fractional derivative. In the present paper, delayed fractional differential equations with bounded time varying coefficients in four different forms are analyzed using series solution and Chebyshev spectral collocation. A fractional differential equation with a known exact solution is then solved by the methodology presented in the paper. The agreement between the two is found to be excellent in terms of point-wise error in the trajectories. Solutions to the described fractional differential equations are computed next in state space and second order forms.