High-order Legendre collocation method for fractional-order linear semi-explicit differential algebraic equations (Q1716835)

The paper deals with a system of linear differential-algebraic equations of rational order. The first result is a theorem with sufficient conditions for the solutions to exist and to be unique. Moreover, the authors discuss the smoothness properties of the solutions. Next, the authors introduce a collocation method for a numerical solution of the equations. The Gauss-Legendre nodes are used as the collocation points. A convergence analysis is provided under some not very explictly stated conditions. Finally, the authors suggest to amend the collocation scheme by a regularization technique in order to improve the convergence order.