This present work is devoted to investigate the transient phenomena for a novel mathematical model of elasto-thermodiffusion in an isotropic three-dimensional thermoelastic medium subjected to permeating gas induced by a rectangular thermal pulse, where the heat conduction equation is defined in an integral form of a common derivative involving a nonsingular kernel interval by incorporating the Caputo-Fabrizio (CF) heat transfer law. The time-dependent chemical potential is also assumed to be known on the bounding plane. Employing the Laplace transform and double-Fourier transform techniques, the problem has been solved analytically in the transformed domain. Numerical inversion of the Laplace transform and double-Fourier transforms are carried out using a Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of the CF parameter and thermodiffusion also.