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Description
This work investigates heavy quark dynamics within the quark-gluon plasma (QGP) by incorporating memory effects through a generalized Langevin equation. We model time-correlated thermal noise with a power-law decay using a fractional differential equation based on the Caputo fractional derivative of order parameter (\nu ). To calculate the impact of memory, we systematically evaluate the momentum correlation, the time evolution of the average squared momentum, the average squared displacement, and the average kinetic energy. Furthermore, we analyze how memory affects the higher normalized central moments of the heavy quark transverse-momentum distribution. Our findings demonstrate that time-correlated thermal noise substantially alters heavy quark dynamics, highlighting the critical role of memory effects in modeling QGP evolution.