  We study the thermodynamic properties of massless Dirac fermions in graphene
under a uniform magnetic field and Rashba spin-orbit coupling with a
$q-$deformed Heisenberg algebra calculus. The thermodynamic functions such as
the Helmholtz free energy, total energy, entropy and heat capacity are obtained
by using an approach based on the zeta function and Euler-Maclaurain formula.
These functions will be numerically examined for different values of
$\eta={1\over i}\ln(q)$. In particular, the heat capacity in the presence of
deformation, all curves coincide and reach the fixed value $C=6K_B$ three times
greater compared to the case of undeformed massless Dirac fermions in graphene.
