Change in the free volume of an elastomer is modelled to predict the physical ageing of filler reinforced rubber by a nonlinear, fractional differential equation as a function of physical ageing temperature and physical ageing time. Elastomers undergo physical ageing after a temperature alteration when the molecules, out of thermodynamic equilibrium, tend to recover their equilibrium state resulting in the evolution of free volume towards its equilibrium value. The effects of physical ageing were thought to be restricted to temperature changes at low temperatures. Conversely, it has been discovered that for the case of filled elastomers, physical ageing is also associated to temperature alterations at normal temperatures. In this paper, a novel free volume differential equation for physical ageing of filled rubbers is developed. The developed free volume equation can then be used in the constitutive equations to predict the material properties for filler reinforced rubber more accurately.