State-Space Approach to the Time-Fractional Maxwell’s Equations under Caputo Fractional Derivative of an Electromagnetic Half-Space under Four Different Thermoelastic Theorems

Abstract

This paper introduces a new mathematical modelling method of a thermoelastic and electromagnetic half-space in the context of four different thermoelastic theorems: Green–Naghdi type-I, and type-III; Lord–Shulman; and Moore–Gibson–Thompson. The bunding plane of the half-space surface is subjected to ramp-type heat and traction-free. We consider that Maxwell’s time-fractional equations have been under Caputo’s fractional derivative definition, which is the novelty of this work. Laplace transform techniques are utilized to obtain solutions using the state-space approach. Laplace transform’s inversions were calculated using Tzou’s iteration method. The temperature increment, strain, displacement, stress, induced electric field, and induced magnetic field distributions were obtained numerically and are illustrated in figures. The time-fraction parameter of Maxwell’s equations had a major impact on all the studied functions. The time-fractional parameter of Maxwell’s equations worked as resistant to the changing of temperature, particle movement, and induced magnetic field, while it acted as a catalyst to the induced electric field through the material. Moreover, all the studied functions have different values in the context of the four studied theorems.