Basically, you'll want to use a perspective-based method of drawing shadows, such as the technique I demonstrated here:
How to calculate the shadow direction, size, and transparency?
However, you'll need to be doing a modification on your perspective lines to match the distortion you're doing for the perspective in general. If I'm reading your sketch correctly, you've drawn a warped/wavy grid that represents the perspective, so your light perspective lines would have to "snap" to that same grid. In the end, this just means the the shadows that fall on the ground or objects will curve along the same paths as everything else, and be as "straight" as your sidewalk is.
Keep in mind, though, that the sun is very high in the sky, which likely means that your light source point will be well off your page (unless you're drawing the sun in a low position like setting/rising, then it may very well be on your page).