In the present study, in order to provide some flexible and more appropriate tools which can better describe cases of the dynamics with memory effects or of nonlocal phenomena, a novel mathematical model of elasto-thermodiffusion introduced in the context of Taylor’s series expansion involving memory-dependent derivative of the function for the dual-phase-lag heat conduction law is proposed. The governing equations of this new model are applied to a one-dimensional half-space, which is taken to be traction free and is subjected to different time-dependent thermal loadings (thermal shock, periodically varying thermal loading and ramp-type heating) and chemical shocks.