Can newtons second law be applied in a non-inertial frame of reference

yes , u can apply newtons 2nd law in a non-inertial frame but u hav to consider the pseudo force and modify the equation accordingly

for example ,

we can take a non inertial frame which has only transational acceleration  say 'α'...

then 2nd law equation get modified to

m*dv/dt = F - mα

thus u can see here there is only a simple modification u hav to consider.....

Yes,newton's second law can be applied in non-inertial frame of reference by taking proper pseudo forces in consideration.

Non-inertial frame is accelerated frame,so you take system having pseudo acceleration opposite to the acceleration of the  frame & equal in magnitude.

It could be equivalently stated that you make the non-inertial frame an inertial one the moment you take opposite acceleration working on the system(pseudo accⁿ & force)