Motion Of A Body In A Resisting Medium Using Fractional Calculus Approach


In this manuscript we propose a fractional differential equation to describe the vertical motion of a body through the air. To keep the dimensionality of the physical parameter in the system, an auxiliary parameter σ is introduced. This parameter characterizes the existence of fractional components in the given system. We prove that there is a relation between γ and σ through the physical parameter of the system and that, due to this relation the analytical solutions are given in terms of the generalized Mittag-Leffler function depending on the order of the fractional differential equation.

Keywords: – Fractional calculus: generalized Mittag-Leffler function.

Kishan Sharma, Brijesh Kumar Gupta, Manoj Sharma