Abstract
In this article, a modified Moore–Gibson–Thompson heat transfer equation with a memory-dependent derivative is utilized to investigate the thermoelastic interaction induced by non-Gaussian lasers in an infinitely elastic nonlocal medium. A memory-based derivative is also examined, and it was discovered to be superior at predicting the pattern of real-life challenges. This finding is part of the conviction that is currently analyzed. The idea of a memory-dependent derivative is attractive since it has some peculiarities. These characteristics include remarkable components as the kernel function and time lag, both of which can be freely selected according to the specifications of the problem. In addition, the non-local concept of Eringen was utilized in the research project so that the small-scale influence could be understood. Using the Laplace transform as a method, analytical–numerical solutions to problems involving thermo-physical fields, such as dimensionless temperature and deformation, as well as nonlocal physical stress, can be analyzed and compared. Numerical solutions have been used to explore the influence of memory-dependent derivative components such as the kernel function and the time delay coefficient on the studied domain variables of the medium. The computational outcomes of the studied fields are also used to find out the role of the non-local index.