Abstract <p>Recent breakthroughs in memory-dependent and fractional-order formulations address fundamental inadequacies in classical theory. Fractional derivatives capture hereditary effects and spatial nonlocality, but memory-dependent derivatives (MDDs) allow more flexibility and interpretability by integrating kernel-defined delay mechanisms. To assist engineers and scientists in designing next-generation thermal systems, this effort aims to provide a robust and proven framework that incorporates a solid structure using memory-dependent derivatives (MDDs). Many studies have been conducted so far that have used a cylindrical-shaped structure for thermal investigations, but there is still a tremendous opportunity to modify the structural design by using a rectangular-shaped plate, which is capable and significant for the advancement of the research and is critical for contemporary design issues in infrastructure, nuclear, and aerospace engineering. This confirmed framework can only be potentially observed by creating a more precise modeling of the heat transfer equation in the light of a circular laser beam moving heat source with uniform distribution utilizing MDDs for a thin rectangular plate structure. The desired solution to the heat transfer equation (HTE) is found by applying the Laplace transformation to memory derivatives and the Fourier transform method to spatial variables. The effects of thermal stress on the plate are also assessed using the ensuing moments and forces. The&#xa0;temperature, deflection, and stress function results are visually shown for various time-delay parameters, kernel function options, laser-moving heat sources with varied laser powers, and scan speeds. The computing investigation examines a plate with copper-based material characteristics. Finally, the proposed mathematical modeling employing MDDs is revolutionizing heat transfer in materials exposed to laser pulses, especially in industries where precision, speed, and thermal control are critical.</p>