Abstract
In this work, the restricted three-body system is studied in the framework of the continuation fractional potential with its application on the Earth-Moon system. With the help of a numerical technique, we obtained thirteen equilibrium points, such that nine of them are collinear while the remaining four are non-collinear points. We found that the collinear points near the smaller primary were shifted outward from the Moon, whereas the points near the bigger primary were shifted towards the Earth as the value of the continuation fractional parameter increased. We analyzed the zero-velocity curves and discussed the perturbation of the continuation fractional potential effect on the possible regions of the motion. We also discussed the linear stability of all the equilibrium points and found that out of thirteen only two were stable. Due to such a prevalence, the continuation fractional potential is a source of significant perturbation, which embodies the lack of sphericity of the body in the restricted three-body problem