As we know acceleration is frame dependent and force is frame independent. In Newton's Second Law of Motion, how can we write $F = ma$? Doesn't that imply Frame independent = frame dependent?
For inertial frames of references, $ F=ma$ holds true. For non-inertial frames, to balance this equation with the new relative acceleration $a'$, you need to add pseudo forces, as in, $ F= ma' + F'$. An example of this pseudo force would be the centrifugal force, which comes into the equation when you observe things from a rotating frame of reference.
"Frames" are more of relativistic concept than a Newtonian one. In Newtonian physics, there's One True Frame. If we add Galilean boosts to Newtonian physics, acceleration and force are both frame independent. In relativity, both acceleration and force are frame dependent. In both of them, $F=ma$ (if $m$ refers to relativistic mass).