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

Abstract

PurposeThe purpose of this paper is to deal with a new generalized model of thermoelasticity theory with memory-dependent derivatives (MDD).Design/methodology/approachThe 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.FindingsThe solutions are presented graphically for different values of time delay and kernel function.Originality/valueThe 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.