Hyperbolic Two Temperature Fractional-Order Thermoelastic Model Subjected to Thermal Loading with Two Relaxation Times

The present work investigates the thermoelastic behaviour of an elastic material occupying the half space subjected to shock wave in the context of the fractional order generalized thermoelasticity associated with two relaxation times. The Laplace transform together with the Laplace transform of Caputo fractional integral has been applied to solve the closed form of the obtained solutions in the Laplace transform domain. The inversion of the dimensionless physical quantities are obtained numericaly using a complex inversion formula of Laplace transform based on a Fourier expansion. The variation of the heat conduction, the distribution of the stress and the strain with the fractional order parameter, second relaxation time and time are studied and the results presented graphically. Comparison between the effects of different parameters has been illustrated graphically.