The linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative. The order of the derivative being considered is 0 ≤ v ≤ 1. At the lower end v 0 the equation represents an undamped oscillator and at the upper end v 1 the ordinary linearly damped oscillator equation is recovered. A solution is found analytically, and a comparison with the...

In road traffic collisions, pedestrian injuries and fatalities account for approximately 11% and 20% of casualties in the USA and the EU, respectively. In many less motorised countries, the majority of victims are pedestrians. The significant influences of vehicle speed, pedestrian speed and pedestrian gait on pedestrian post-impact kinematics have been qualitatively noted in the literature, bu...