Purpose <p>The main purpose of this study is to present a novel application of the new and improved version of the memory-dependent derivative within the framework of a generalized thermoelastic model, with the objective of uncovering new insights into the characteristics associated with the memory-dependent derivative. The dual phase lag model has been incorporated into the study. The thermoelastic response to thermal shock in a homogeneous, orthotropic, magneto-thermoelastic medium is analyzed using a novel mathematical framework that accounts for memory effects.</p> Methods <p>The problem is systematically approached by first applying Laplace and Fourier integral transforms to the governing equations. This process leads to the derivation of a system of ordinary differential equations, which is then expressed in a compact vector-matrix form. Solutions in the transformed domain are obtained using the eigenvalue method. Subsequently, the thermophysical quantities in the space-time domain are computed using suitable numerical techniques.</p> Results <p>The numerical solutions are presented in graphical form. Given the pivotal role of the kernel function within the memory-dependent derivative, a comparison between the previous and improved versions of the memory-dependent derivative is presented, considering the influence of different kernel functions on the outcomes. A comparison of outcomes from the Lord-Shulman and dual phase lag models, along with previous and improved versions of the memory-dependent derivative, is presented. Results without the memory-dependent derivative are presented to assess its influence.</p> Conclusions <p>This study advances the mathematical approach to addressing memory effects in thermoelasticity by employing a new version of the memory-dependent derivative. The resulting patterns and numerical findings offer novel insights into thermophysical behavior, paving the way for future research on complex material responses.</p>