Numerical analysis for distributed-order differential equations

In this paper we present and analyse a numerical method for the solution of a distributed-order differential equation of the general form ∫0mA(r,D∗ru(t))dr=f(t) where mm is a positive real number and where the derivative D∗r is taken to be a fractional derivative of Caputo type of order rr. We give a convergence theory for our method and conclude with some numerical examples.