Like in Newtonian kinematics, the relativistic change of reference frame must be a vector system of transformation laws for position, velocity and acceleration.

In special relativity, when changing the reference frame the coordinates of a moving point is transformed using Lorentz transformation. But the velocity-addition formula that transforms velocity is in a too different mathematical form than the Lorentz transformation. And for acceleration, there is not a transformation at all. The theory of Time relativity that I develop provides a coherent vector system of transformation laws for position, velocity and acceleration

Read the article below.

https://www.academia.edu/42973353/Relativistic_kinematics_and_gravitation

https://pengkuanonphysics.blogspot.com/2020/05/relativistic-kinematics-and-gravitation.html