How to modify Axes Style/Ticks of RegionPlot?

Question

Could one modify the output of the following

  z1 = RegionPlot[ p > Sin[q], {p, 0, 2}, {q, 0, 2}, PlotStyle -> Brown,
    AxesLabel -> {"S", "T"}];
z2 = RegionPlot[ (p > Sin[q^2]), {p, 0, 2}, {q, 0, 2}, 
   PlotStyle -> Gray, AxesLabel -> {"S", "T"}];
Show[z2, z1 ]

to something like this:

with preferably arrow heads at the end of axes? The marks on horizontal and vertical axes are where I want to write $\beta$ and $\alpha$.

Answer 1

Edit

Clear[z1, z2];
z1 = RegionPlot[p > Sin[q], {p, 0, 2}, {q, 0, 2}, PlotStyle -> Brown, 
   AxesLabel -> {"S", "T"}, BoundaryStyle -> None];
z2 = RegionPlot[(p > Sin[q^2]), {p, 0, 2}, {q, 0, 2}, 
   PlotStyle -> Gray, AxesLabel -> {"S", "T"}, 
   Ticks -> {{{1.5, Style[α, 16]}}, {{1, Style[β, 16]}}},
    Frame -> False, Axes -> True, AxesStyle -> Arrowheads[{{0.05}}], 
   PlotRangePadding -> .2, BoundaryStyle -> None];
Show[z2, z1]

FrameTicks -> {{{{1.5, α}}, None}, {{{1, β}}, None}}

z1 = RegionPlot[p > Sin[q], {p, 0, 2}, {q, 0, 2}, PlotStyle -> Brown, 
   AxesLabel -> {"S", "T"}];
z2 = RegionPlot[(p > Sin[q^2]), {p, 0, 2}, {q, 0, 2}, 
   PlotStyle -> Gray, AxesLabel -> {"S", "T"}, 
   FrameTicks -> {{{{1.5, Style[α, 16]}}, 
      None}, {{{1, Style[β, 16]}}, None}}];
Show[z2, z1]