Physical properties of the projectile motion using the conformable derivative

Abstract

In this paper, the projectile motion in a resisting medium has been investigated by using the conformable derivative. In order to preserve the dimensionality of the physical quantities, an auxiliary parameter sigma, which has a dimension of seconds, was imposed in the fractional derivative. The converted FDEs have been analytically solved. In the literature, some authors have suggested some relations between the auxiliary parameter sigma and the resistant parameter k. Their procedure is a special case in view of the current results. So, it has been proved in this paper that the dimensions of the physical quantities are always correct without any further assumptions that relate sigma with k. Moreover, it is shown in this paper that the fractional order has no effect neither on the trajectory nor on the range of the projectile, i.e., unlike the corresponding previous results. However, the flight time of the projectile depends on the non-integer order a of the conformable derivative. The impacts of the involved parameters on the projectile properties are discussed through tables and several graphs. The values of the range and the flight time are tabulated for the purpose of comparisons with a previous work in the literature and also with the experimental data. Hence, we give some light on the difference between the conformable derivative and the other definitions when applied on the projectile problem.