Derivative analysis of fractional order on reflection of p-waves with electromagnetic, temperature, and initial stress with three-phase-lag

In this paper, the three-phase-lag model of fractional analysis on the reflection of two-dimensional problem of p-waves with initial stress, temperature-dependent, and magnetic field is investigated. The formulation of the problem for an isotropic homogeneous medium based on a three phase-lag theory. The boundary conditions applied on the surface for the stresses and thermal insulation. The numerical solution presented as well as the graphical representation of the impact of analysis considering the external parameters. Also, the modified elastic waves reflected under the action of the magnetic field, initial stress, fractional degree coefficient, and temperature to determine the more exact nature of the reflection of these waves, particularly seismic waves. A comparison has been made between the results obtained and the previous results obtained by others and already published and are in agreement with these, when external parameters considered in the present investigation neglected. The results obtained indicate that the new external parameters have new impact on the waves reflection and applicable in diverse fields as engineering, earthquakes, volcanos, geophysics, acoustics, and astronomy.