A computational matrix method for solving systems of high order fractional differential equations

In this paper, we introduced an accurate computational matrix method for solving systems of high order fractional differential equations. The proposed method is based on the derived relation between the Chebyshev coefficient matrix A of the truncated Chebyshev solution u(t)$\mathbf{u}(\mathbf{t})$ and the Chebyshev coefficient matrix A^(ν)${\mathbf{A}}^{(\nu )}$ of the fractional derivative u^(ν)${\mathbf{u}}^{(\nu )}$. The fractional derivatives are presented in terms of Caputo sense. The matrix method for the approximate solution for the systems of high order fractional differential equations (FDEs) in terms of Chebyshev collocation points is presented. The systems of FDEs and their conditions (initial or boundary) are transformed to matrix equations, which corresponds to system of algebraic equations with unknown Chebyshev coefficients. The remaining set of algebraic equations is solved numerically to yield the Chebyshev coefficients. Several numerical examples for real problems are provided to confirm the accuracy and effectiveness of the present method.