Fractional parameters, often related to fractional calculus, introduce nonlocal and memory-dependent effects into the modeling of functionally graded elliptical plates made from thermally sensitive materials. These parameters affect the mechanical and thermal response by capturing complex behaviors such as anomalous diffusion of heat and viscoelastic or thermoelastic memory effects that classical integer-order models cannot represent. Specifically, fractional derivatives in the governing equations modify stiffness, damping, and thermal conduction characteristics, leading to altered vibration frequencies, stress distributions, and thermal deformation patterns. In thermally sensitive functionally graded materials (FGMs), where material properties vary continuously and depend on temperature, fractional parameters help model the coupled thermo-mechanical behavior more accurately, reflecting size-dependent and history-dependent effects. This results in more precise predictions of stability, buckling, and dynamic response under thermal loads, especially for elliptical plates where geometry further influences stress concentration and deformation modes. Overall, fractional parameters enhance the fidelity of models for FG elliptical plates under thermal effects by incorporating complex material behavior and nonlocal interactions.