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In this work, we investigate the melting of charmonium states within a holographic QCD model in the context of Einstein-Maxwell-Dilaton (EMD) theory. In the dual field theory, the model describes the heavy mesons inside a finite temperature and density medium. First, we calculate the spectrum at zero temperature. Then, at finite temperature, we obtain the spectral functions, where the heavy vector meson are represented by peaks. We show that the charmonium melts down at temperatures above the confinement/deconfinement temperature of the quark-gluon plasma. We also observe that the chemical potential speeds up the melting process. This finding is in agreement with results previously reported in the literature. In the gravitational side of the theory, we solve the perturbation equations in the hydrodynamics limit. From this result, we read off the diffusion coefficient by comparing the dispersion relation against the corresponding result obtained in the dual field theory. We also investigate the behavior of the diffusion coefficient as a function of the temperature. The perturbation equations are solved numerically, in order to get the quasinormal frequencies. We report the emergence of a new mode whose real part increases rapidly at a certain value of the chemical potential while its imaginary part decreases with the increasing of the chemical potential. Finally, by comparing against results obtained in the conformal plasma, we observe that the real part of the frequency increases, while the imaginary part decreases when we consider the non-conformal plasma.