I started on my own learning about GR and SR two months ago, and I still do not have clear if it is possible or not. The following example was explained to me by someone who affirmed: "SR applies only on inertial reference frames":
Let's imagine we have two different reference frames : A' and A. Reference frame (RF) A' is moving with constant velocity (v), meanwhile RF A has no velocity (A' moves relative to A with constant v).
RF A' has a wire underneath and RF A has an aerial above. When both interact, clocks start running in both RFs (clock A' and clock A) and a light ray emerges (from the wire-aerial interaction and with the same velocity vector direction RF A' has).
Then we agree distance can be determined from both RFs.
i.e. : x = x' + vt'
Then I asked myself: why would not be correct consider the case where A' is an accelerated RF and distance is determined from RF A (i.e.) as x = x' + at'?
My doubts about if "SR applies only on inertial reference frames" sentence was true increased when I checked out more sources and they affirmed accelerated reference frames were possible in SR.