The influence of time-fractional Maxwell’s equations based on Caputo fractional derivative on an electromagnetic solid cylinder under four different thermoelastic theorems

Abstract

This paper introduces a mathematical model of a thermoelastic and electromagnetic solid cylinder in the context of four different thermoelastic theorems: Green–Naghdi type I, type III, Lord–Shulman, and Moore–Gibson–Thompson. One of the main goals is to look at Maxwell’s time-fractional equations using Caputo’s fractional derivative definition and apply them to a one-dimensional cylinder to understand how fractional order effects influence the four different thermoelastic theorems. The bounding plane of the cylinder surface is subjected to ramp-type heat and is connected to a rigid foundation. We apply the techniques of Laplace transforms to obtain solutions through a direct method for one-dimensional governing equations. We have calculated the inversions of the Laplace transform using Tzou’s iteration method. The temperature increment, strain, displacement, stress, induced electric field, and induced magnetic field distributions have been obtained numerically and illustrated in figures. The time-fraction parameter of Maxwell’s equations has a significant impact on all the studied functions. The time-fractional parameter of Maxwell’s equations slows down the increase in temperature, movement of particles, and the created magnetic field, but speeds up the created electric field. The four models studied introduce different values for all the studied functions.