Memory response on thermal wave propagation in an elastic solid with voids due to influence of magnetic field

Fractional derivative is a widely accepted theory to describe the physical phenomena and the processes with memory responses which are defined in the form of convolution having kernels as power functions. Due to the shortcomings of power-law distributions, some other forms of derivatives with few other kernel functions are proposed. This present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for an infinite solid with void under the action of an induced magnetic field due to the presence of a prescribed plane heat source. The heat transport equation for this problem is involving the memory-dependent derivative on a slipping interval in the context of Lord Shulman model of generalized thermoelasticity. Employing the Laplace transform as a tool, the analytical results for the distributions of the change in volume fraction field, temperature and deformations are obtained on solving the vector-matrix differential equation using eigenvalue approach. The numerical inversion of the Laplace transform is performed using the Zakian method. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative and presence of a magnetic field also.