I would like to customize the RegionPlot with the following: Remove thin frame, but remain the ticks and frame labels.
RegionPlot[{x^2 + y^2 < 2, x^2 + y^2 > 2}, {x, 0, 1.5}, {y, -1.5,
1.5}, FrameLabel -> {a, b},
FrameTicks -> {{None, None}, {{1}, None}}]