Electromagnentic filed and rotation for fractional derivative order calculus with temperature-dependent on reflection of longitudinal wave under initial stress and three-phase-lag model

The central interest of the present study is to investigate the fractional order calculus in addition to studying impact of temperature dependent properties, electromagnetic field, rotation, and primary pressure on the reflection of plane and secondary vertically waves phenomenon putting in considerations the three-phase-lag model (THPL). The main equations that have been articulated related to the body forces neglecting the outer temperature supplier and the existence of primary pressure, spin, and the dependent on temperature according to THPL theory in its fractional form (Caputo fractional derivatives). The researchers related the boundary conditions with the consideration of the mechanical and Maxwell's stresses and temperature dependent properties. The researchers have made a comparison between the analytical integer and fractional solutions for the problem. The solutions are calculated analytically and are shown by drawings to demonstrate the physical connotation of the wave's reflection phenomenon. The existence of fractional derivative illustrates the degree to which these waves reach can be employed in today's manufacturing. By comparing the existence and non-existence of fractional derivative demonstrating the way the fractional derivative influences these waves.