Non Inertial Frames and Pseudo (fictitious) forces:
A non-inertial frame of reference is a frame which is not an inertial frame or which is an accelerated frame. In this frame of reference the Newton's Laws of Motion are violated. The example of such a situation is when the brake of a car is abruptly applied to slow down the motion of it. However, the person sitting inside the car experiences a forward movement. This movement occurs due to the fictitious force present in our imagination.
Thus, fictitious force is the pseudo force which come into play in a non-inertial frame of reference when it is treated like inertial frame.
Suppose we are working to solve a problem in frame B. It may be useful to consider the apparent force in this frame, which is given by
where xb = xa – x. Now we can define the fictitious force as: