Analysis of the two-dimensional fractional projectile motion in view of the experimental data

This paper addresses the modeling of projectile motion using fractional models vis-a-vis experimental data. Recently, it was shown that an auxiliary parameter needs to be included in the fractional modeling to preserve the dimensionality of the physical quantities. In previous studies, sigma was subjected to several restrictions without considering clear and meaningful reasons. Such problems are overcome here and a method for estimating sigma using the experimental data is introduced. A new solution for the two-dimensional projectile motion using the Caputo's fractional derivative is obtained. An explicit formula for the trajectory of the projectile in vacuum is first derived. Then, the projectile parametric equations in a resistant medium are expressed in terms of the Mittag-Leffler function. The transcendental equations for the time of flight and the time of maximum height are solved numerically. The model agrees with the classical one as the fractional order tends to 1. In view of the superior results, the current numerical modeling approach is validated for this real-world application.