Numerical Solution of Distributed Order Differential Equations

In this talk we present and analyse a numerical method for the solution of a distributed order differential equation of the general form $$ \int_0^m \mathcal{A}(r, D^r_*u(t)) dr = f(t) $$ where the derivative $D^r_*$ is taken to be a fractional derivative of Caputo type of order $r$. We give a convergence theory for our method and conclude with some numerical examples.