Numerical analysis for 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.