Random walk models associated with distributed fractional orderdifferential equations

In this paper we construct new random walks connected with fractional order differential equations. Namely, the governing equations corresponding to the constructed random walks are multi-term or distributed fractional order differential equations. Nowadays the connection between random walk and fractional order dynamics is well known, see, for instance [1, 17, 26, 33, 38]. A number of constructive random walk models governed by fractional differential equations in the one-dimensional case were studied by Gillis, et al. [12], Chechkin, et al. [7], Gorenflo, et al. [15, 16], and in the n-dimensional case by Umarov [35], Umarov, et al. [36], Andries, et al. [3]. The governing equation in these studies depends on parameters β ∈ (0, 1] and α ∈ (0, 2], and is given by the fractional order differential equation