Abstract
A new mathematical model of generalized thermoelasticity with memory-dependent derivatives for the dual-phase-lag heat conduction law is constructed. The governing equations of the new model are applied to a half-space subjected to ramp-type heating. Laplace transforms technique is used. The solution is obtained for different types of functions representing the thermal shock and for different values of the parameter of the time fraction derivative of the model. The effects of time-delay and arbitrary kernel function on elastic material are studied and represented graphically. The predictions of the theory are discussed and compared with dynamic classical coupled theory.