The freely available FCC package overcomes several limitations of current numerical methods for solving linear FDEs. For instance, the proposed package 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 the Chebyshev polynomials. Then, using two proposed discretization operators for matrix functions results in an explicit form of solution for a system of linear FDEs with discrete delays. Moreover, it is shown that the proposed method can treat two common classes of linear FDEs: a system of linear commensurate order FDEs and a system of linear fractional-order delay-differential equations.
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References in zbMATH (referenced in 1 article )
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- Dabiri, Arman; Butcher, Eric A.: Stable fractional Chebyshev differentiation matrix for the numerical solution of multi-order fractional differential equations (2017)