Polynomial–Sinc collocation method combined with the Legendre–Gauss quadrature rule for numerical solution of distributed order fractional differential equations

In the current work, we present an efficient collocation method based on the polynomial–Sinc combined with the Legendre–Gauss quadrature rule for numerically solving a class of distributed order fractional differential equations. This method uses Lagrange approximation at Sinc points. The main purpose of this work is to generalize polynomial–Sinc method to the fractional calculus. The convergence of our method is discussed. Finally, some test problems are used to verify the accuracy and applicability of the presented method.