In this paper we present and analyse a numerical method for the solution of a distributed-order differential equation of the general form ∫0m A (r, D*r u (t)) d r = f (t) where m is a positive real number and 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. © 2008 Elsevier B.V. All rights reserved.
Diethelm, K., & Ford, N. J. (2009). Numerical analysis for distributed-order differential equations. Journal of Computational and Applied Mathematics, 225(1), 96–104. https://doi.org/10.1016/j.cam.2008.07.018