Fractional thermoelastic diffusion problem for an infinitely long hollow cylinder using the Caputo–Fabrizio definition

Abstract

In the context of the fractional-order theory of thermoelastic diffusion, the problem of a thermoelastic infinitely long hollow cylinder is considered. The outer surface of the cylinder is taken traction free and subjected to thermal shock, while the inner surface is taken to be in contact with a rigid surface and is thermally insulated. The governing equations of the problem are formulated. Laplace transform technique and a direct approach method are used to obtain the solution in transformed domain. A numerical method is used to get the inversion of the Laplace transform of the solutions. The temperature, displacement, stress, and concentration as well as the chemical potential are represented graphically.