This paper deals with the propagation of the plane wave in a nonlocal magneto-thermoelastic semiconductor solid with rotation. The fractional-order three-phase lag theory of thermoelasticity with two temperatures has been applied. When a longitudinal wave is incident on the surface z = 0, four types of reflected coupled longitudinal waves (the coupled longitudinal displacement wave, the coupled thermal wave, coupled carrier density wave, and coupled transverse displacement wave) are identified. The plane wave characteristics such as phase velocities, specific loss, attenuation coefficient, and penetration depth of various reflected waves are computed. The effects of two temperatures, non-local parameter, fractional order parameter, and Hall current on these wave characteristics are illustrated graphically with the use of MATLAB software.

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The aim of the present investigation is to examine the memory-dependent derivatives (MDD) in 2D transversely isotropic homogeneous magneto thermoelastic medium with two temperatures. The problem is solved using Laplace transforms and Fourier transform technique. In order to estimate the nature of the displacements, stresses and temperature distributions in the physical domain, an efficient approximate numerical inverse Fourier and Laplace transform technique is adopted. The distribution of displacements, temperature and stresses in the homogeneous medium in the context of generalized thermoelasticity using LS (Lord-Shulman) theory is discussed and obtained in analytical form. The effect of memory-dependent derivatives is represented graphically.

The present research deals with the propagation of Rayleigh wave in transversely isotropic magneto-thermoelastic homogeneous medium in the presence of mass diffusion and three-phase-lag heat transfer. The wave characteristics such as phase velocity, attenuation coefficients, specific loss, and penetration depths are computed numerically and depicted graphically. The normal stress, tangential stress components, temperature change, and mass concentration are computed and drawn graphically. The effects of three-phase-lag heat transfer, GN type-III, and LS theory of heat transfer are depicted on the various quantities. Some particular cases are also deduced from the present investigation.

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This investigation is focused on the study of thermomechanical interactions in homogeneous transversely isotropic magneto thermoelastic medium with fractional order heat transfer and hall current. As an application, the bounding surface is subjected to normal force with weak, normal and strong conductivity. Laplace and Fourier transform is used for solving field equations. The analytical expressions of temperature, displacement components, stress components, and current density components are computed in the transformed domain. The effects of hall current and fractional order parameters by varying different values are represented graphically. Some specific cases are also figured out from the current research.