There are several types of central-force problems, depending on the physical theory being applied.
Classical physics
Classical central-force problem Kepler problem, a special case (inverse-square central force) Two-body problem, which may be reduced to a central-force problem
General relativity
Schwarzschild solution, the geodesics of the Schwarzschild metric
Quantum mechanics
Hydrogen-like atom, a special case (inverse-square central force)