Transient response of a magneto-thermo-viscoelastic medium with Seebeck–Peltier coupling: A conformable fractional-order approach

This study investigates the influence of an external magnetic field and conformable fractional-order effects on a two-dimensional generalized thermo-viscoelastic medium characterized by a single relaxation time. The governing equations are developed within the framework of fractional thermoelasticity, incorporating viscoelastic damping and thermoelectric interactions. The coupling between electrical, thermal, and mechanical fields is introduced through a generalized Ohm’s law that accounts for charge density and the temperature-gradient–induced electromotive force (Seebeck effect), together with heat transport governed by Fourier’s law augmented by the Peltier contribution. The formulation enables analysis of magneto–thermo-viscoelastic responses under combined electromagnetic and thermal stimuli. The numerical results and figures are obtained by using normal mode analysis technique in addition, we analyzed different fractional parameter values and reviewed the results with and without viscosity and (Seebeck-Peltier) coefficients. MSC 2020 35R11, 74F15, 74F05, 80A17