Fractional Chebyshev collocation method (original) (raw)

The fractional Chebyshev collocation (FCC) method is an efficient spectral method for solving a system of linear fractional-order differential equations (FDEs) with discrete delays. The FCC method overcomes several limitations of current numerical methods for solving linear FDEs. For instance, the FCC method can be used for linear incommensurate order FDEs and it does not require to be in canonical form. The essence of the method is that a discretization of the solution at the Chebyshev Gauss–Lobatto collocation points results in having spectral convergence and smaller computation time compared to finite difference methods. To accomplish this, a fractional differentiation matrix is derived at the Chebyshev Gauss–Lobatto collocation points by using the discrete orthogonal relationship of th