For massive particles, force translates into acceleration which again is a change of the velocity vector in direction and/or magnitude.
For a photon, the velocity magnitude cannot change, only the direction. It curves towards the geodesicsource of gravitaion, which, I think, can be compared to a force acting at some angle to the velocity direction. If it is not a right angle, a massive particle would increase its velocity's magnitude. We can get the velocity vector by integation of the acceleration. The photon instead, I assume, changes its frequency. Can the combined velocity/frequency pair be derived also by simple integration? Of what?