It seems to me the current description of fictitious forces is too complicated. It is described as effect of accelerate non inertial frame and there are four types of fictitious forces: rectilinear acceleration force, centrifugal force, Coriolis force and Euler force. Why cant we say that there is only one fictitious force and this force is acting on accelerating object in opposite direction to direction of acceleration? Sounds much easier to me, covers all four types of fictitious forces and you dont need this complicated and redundand babble about reference frames. It would be much easier to understand.