Piecewise polynomial collocation methods for system of weakly singular Volterra integral equations of the first kind: application to the system of fractional differential equations

We apply discontinuous piecewise polynomial collocation methods for solving system of weakly singular Volterra integral equations of the first kind. We use the graded mesh for ap- plying such methods. The graded mesh show a higher order of convergence than the uniform mesh known as \superconvergence . Then, we apply a relevant method to a system of frac- tional differential equations. The numerical experiments show the efficiency of the methods.