Modeling of memory-dependent derivatives with the state-space approach

The purpose of this paper is to deal with a new generalized model of thermoelasticity theory with memory-dependent derivatives (MDD).

The two-dimensional equations of generalized thermoelasticity with MDD are solved using a state-space approach. The numerical inversion method is employed for the inversion of Laplace and Fourier transforms.

The solutions are presented graphically for different values of time delay and kernel function.

The governing coupled equations of the new generalized thermoelasticity with time delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to a two-dimensional problem of an isotropic plate.