Memory time effect on electromagnetic-thermoelastic materials

In this work, new mathematical model of Maxwell’s equations in an electromagnetic field is derived using the physical principles of fractional calculus. The advantage of our model appears according to the comparison between our model and a previous fractional electromagnetic model which was introduced by Gomez et al. Our model is applied to fractional thermoelastic material associated with one relaxation time interaction due to periodically varying heat source. The Laplace–Fourier double transform technique has been used to get the solution. The inversion of the Fourier transform has been done using residual calculus, where poles of the integrand are obtained numerically in a complex domain using Leguerre’s method and the inversion of the Laplace transformation is done numerically using a method based on a Fourier series expansion technique. Numerical results of temperature, displacement, stress, strain, and induced electric/magnetic fields are obtained for a hypothetical material. Finally, some comparisons have been shown in figures to estimate the effect of fractional-order parameters on all the studied variable fields.