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.