This is not a mathematical question, although there is a mathematical (trigonometric) expression that determines the angular velocity of the sun's rotation at different latitudes.
The main factor for differential rotation is that the sun is so hot that it's entirely or largely gaseous. So it's basically a rotating fluid. (Jupiter and Saturn are also largely gaseous so they're basically rotating fluids, too.)
Another factor is convection caused by the high temperature gradients between the core and the atmosphere. The convection causes internal movements of massive amounts of plasma and the shifting of such masses affects the angular momentum which, by laws of physics, has to be conserved. This energetic shifting reduces the angular momentum with increasing latitude, so it takes longer for a hypothetical point on a surface away from the equator to complete its "day". You could call this effect "drag".
Also, some mass of the sun is radiated into space so the mass of the sun is not constant. Mass, or rather energy, has to be conserved and mass is constantly being converted into electromagnetic energy on many wavelengths by the nuclear reactions taking place around the core, and helium is being formed from fusion of hydrogen. This is the engine driving convection and the steep temperature gradients.
A hypothetical point on the sun's equator rotates once in about every 25 hours, but with increasing latitude towards the poles this slows to about 35 hours for a hypothetical point on the surface approaching the poles.
