Two temperature generalized thermoelasticity involving memory-dependent derivative under fuzzy environment

Abstract

A one-dimensional two-temperature model of generalized thermoelasticity theory in half-space has been studied in this present discussion with memory-dependent derivative. The fuzzy approach has been applied to construct the governing equations. The fuzzy variables such as stress, strain and so on are represented in r-cut. The coupled partial differential equations' analytical solutions are obtained in Laplace transform domain subject to a stress-free boundary with a time-dependent imprecise thermal shock. A suitable numerical inverse Laplace transformation technique is applied to get the space time-domain results for different time delay parameter values and several kernel functions. Two examples of numerical results in the fuzzy environment are performed and are compared with the crisp results graphically. The concluding remarks are made based on numerical results and graphs.