FRACTIONAL MOMENTUM BALANCE EQUATION FOR A VARIABLE-MASS DYNAMICS

Abstract

A new mechanical framework is introduced to describe bodies with time-continuous mass variation, incorporating a functional dependence on mass. In this approach, the dynamics are governed by momentum balance equations formulated using Caputo fractional derivatives, which adhere to a weak form of Galilean invariance. The formulation is particularly focused on the Meshchersky kinetics, accounting for both mass and velocity changes. As a practical example, this paper presents a novel model for the motion of a material body with continuously varying mass in a constant gravitational field—leading to a time-fractional version of the Tsiolkovsky rocket equation, augmented by a dissipative term. Under time-based approximation, deviations from vertical projectile motion are analyzed to assess the internal consistency of the proposed model.