Generalized thermoelasticity with memory-dependent derivatives involving two temperatures

A new generalized model of two-temperature thermoelasticity theory with time-delay and Kernel function is constructed. Taylor theorem in terms of memory-dependent derivatives is proved. The governing coupled equations of the new generalized thermoelasticity with time-delay and Kernel function, which can be chosen freely according to the necessity of applications, are applied to a one-dimensional problem of a half-space. The bounding surface is taken to be traction free and subjected to a time-dependent thermal shock. Laplace transforms technique will be used to obtain the general solution in a closed form. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusions about the new theory have been constructed. Some comparisons are shown in the figures to estimate the effects of the temperature discrepancy and time-delay parameter on all of the studied fields.