Is it possible to derive Newtonian equations of motion with memory?

In this paper for a given example we proved that the Riemann-Liouville fractional integral term appears naturally and relates the external force with acceleration within the fractional Newtonian equation. The consideration of some self-similar process that leads to the fractional integral as well as some possible generalizations of the proposed model was discussed. © Springer Science+Business Media, LLC 2010.