Random-time processes governed by differential equations of fractional distributed order

In view of the previous results it is natural to consider diffusion-type fractional equations of distributed order. We present here an approach to their solutions in terms of composition of the Brownian motion B(t), t > 0 with the random time T∼ν1,ν2. We thus provide an alternative to the constructions presented in Mainardi and Pagnini [19] and in Chechkin et al. [6], at least in the double-order case.