On the generalized Hardy-Hardy-Maurer model with memory effects

In this paper, we reconsider the Hardy-Hardy-Maurer model for the heat propagation in nonlinear rigid conductors in the framework of fractional thermoelasticity, taking into account memory effects. We therefore obtain nonlinear time-fractional telegraph-type equations that are linearizable by change in variable. We discuss in detail two different models in the context of the more general theory of Gurtin and Pipkin of heat propagation with memory. We finally show that a similar derivation of linearizable fractional telegraph-type equations of higher order can be obtained also in the physics of dielectrics.