  We investigate within the formalism of Symplectic Quantum Mechanics a
two-dimensional non-relativistic strong interacting system that represents the
bound heavy quark-antiquark state, where it was considered a linear potential
in the context of generalized fractional derivatives. For this purpose, it was
solved the Schr\"odinger equation in phase space with the linear potential. The
solution (ground state) is obtained, analyzed through the Wigner function
comparing with the original solution, the Airy function for the meson
$c\overline{c}$. The identified eigenfunctions are connected to the Wigner
function via the Weyl product and the Galilei group representation theory in
phase space. In some ways, compared to the wave function, the Wigner function
makes it simpler to see how the meson system is non-classical.
