Abstract

Projectile motion is studied using fractional calculus. Specifically, a newly defined fractional derivative (the Leibniz L-derivative) and its successor (Λ-fractional derivative) are used to describe the motion of the projectile. Experimental data were analyzed in this study, and conclusions were made. The results of well-established fractional derivatives were also compared with those of L-derivative and Λ-fractional derivative, showing the many advantages of these new derivatives.

Highlights

  • When we find the solution of this ordinary differential equation (ODE) in Λ-space, we can return to the initial space by the inverse transformation: Λ2−1 { F ( T )} = F (t)

  • We would like to present some results from a very interesting article [31] that tried to model this motion with well-established fractional derivatives

  • The minimum measure of the case we studied with this projectile motion through using the Caputo derivative was found to be 1209.38 for γ = 1.99

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Summary

Introduction

Fractional differential equations in the initial space are transformed in ODEs in Λ-space This advantage is revolutionary, since no complex methodologies (i.e., application of Mittag–Leffler functions, etc.) are needed to solve these FDEs in the initial space. Γ where 0 It is the right Riemann–Liouville fractional integral over time for 0 ≤ γ ≤ 1 With this transformation, the function f (t) is converted from initial space to an intermediate space function F(t). A Λ-fractional differential equation (Λ-FDE) in initial space can be converted to one with classical derivatives in Λ-space and can be solved as a classical ordinary differential equation (ODE) with unknown function F(T).

Application of Projectile Motion with Least Resistance
Conclusions

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