Abstract
A mathematical model of electro-thermoelasticity has been constructed in the context of a new consideration of heat conduction with memory-dependent derivative. The governing coupled equations with time-delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to several concrete problems: (i) a problem of time-dependent thermal shock; (ii) a problem for a half-space subjected to ramp-type heating and (iii) a problem of a layer media. Laplace transform techniques are used. According to the numerical results and its graphs, conclusion about the new theory has been constructed. The predictions of the theory are discussed and compared with dynamic classical coupled theory. The result provides a motivation to investigate conducting thermoelectric materials as a new class of applicable materials.