Linking a related post and some code to play with below, FWIW.
Not all the LaTeX fraction options you’ve listed seem to be available in Plots gr() renderer.
using LaTeXStrings, Plots; gr(size=(200,100))
plot(lims=(-1,1), framestyle=:none)
annotate!(-1, 0, L"\dfrac{3}{2}")
annotate!(0, 0, L"e^{\frac{1}{2} + c}")
annotate!(1, 0, L"\frac{3}{2}")
