Fractional transient thermal mixed boundary value problem of distributed order

Abstract

In this paper, we introduce the fractional transient thermal mixed boundary value problem of distributed order. We employ the Cagniard-de Hoop and the Wiener-Hopf techniques to solve this problem. The Laplace and Fourier transforms are used to present the formal solution of this problem in terms of some special functions. The numerical simulation of a model example is also given for the heat flow through the foundation of building. KEYWORDS boundary value problem, Cagniard-de Hoop method, distributed order, Fourier transform, Laplace transform, Wiener-Hopf method 6726