Two dimensional fractional projectile motion in a resisting medium

Abstract

Abstract:In this paper we propose a fractional differential equation describing the behavior of a two dimensional projectile in a resisting medium. In order to maintain the dimensionality of the physical quantities in the system, an auxiliary parameter was introduced in the derivative operator. This parameter has a dimension of inverse of seconds ( ) −1 and characterizes the existence of fractional time components in the given system. It will be shown that the trajectories of the projectile at different values of γ and different fixed values of velocity 0 and angle θ, in the fractional approach, are always less than the classical one, unlike the results obtained in other studies. All the results obtained in the ordinary case may be obtained from the fractional case when γ = 1.

Re-Evaluating the Classical Falling Body Problem

“…In recent years, the classical falling body problem (FBP) and the two-dimensional projectile motion [1][2][3][4][5][6][7][8][9][10][11] have been re-evaluated. The FBP has been modeled as the vertical motion of a particle near to the Earth's gravitational field [12][13][14]; that is, as a problem formulated in one dimension.…”

Analysis of the transient state in a parallel circuit of the class RLC

“…where: C j , D j , E j , F j , G j , H j -appropriate complex partial fraction decomposition coefficients (residues) of relations (7) -(11) , ϕ, γ , δ, η, ε, φ -arguments of the complex coefficients C j , D j , E j , F j , G j , H j calculated analogously to formulae (35) and (36) .…”

“…However, recent few decades have shown a great interest in the application of the fractional calculus for various scientific disciplines and problems, eg. in bioengineering [23] , biology [41,42] , medicine [43] and physics [35] . Other technical sciences have also witnessed a significant interest in the application of fractional calculus for different purposes.…”

The Exact Solution of the Falling Body Problem in Three-Dimensions: Comparative Study

“…In the past decades, some attention was given to the study of the falling body problem [1][2][3] and two-dimensional projectile motion [4][5][6][7][8][9][10][11][12][13][14]. In the literature [1][2][3], the falling body problem was modeled as the vertical motion of a particle near the Earth's gravitational field, i.e., as a problem formulated in one dimension.…”