  We study the dependence of beta-function on running coupling constant in
holographic models supported by Einstein-dilaton-Maxwell action for light and
heavy quarks. Although, in the previous paper [arXiv:2402.14512], we considered
different types of the dilaton boundary conditions, but since the behavior of
$\beta$-function as a function of running coupling does not depend
significantly on the boundary condition, we chose one. The corresponding
$\beta$-functions are negative and monotonically decreasing functions, and have
jumps on the 1-st order phase transitions for both light and heavy quarks. In
addition, we compare our holographic results for $\beta$-function as a function
of running coupling with perturbation results that obtained within 2-loop
calculations.
