Three-dimensional projectile motion: analytical solution and numerical treatment of the fractional case

This paper focuses on deriving analytical solutions for three-dimensional projectile motion and investigating numerical approaches for handling these solutions. We derive the equations of projectile motion using both classical and fractional calculus, considering scenarios with and without air resistance. We analyze the characteristics of the projectile's trajectory in both classical and fractional scenarios, providing a comparative study between them. Additionally, we propose an extrapolation method tailored to the nature of the motion equations to estimate projectile trajectories. The accuracy of our proposed method is assessed through the absolute error between exact and numerical solutions, with numerical examples provided to validate the theoretical analysis.

Keywords:

Three-dimensional projectile motion , fractional calculus , Caput\'{o}s fractional derivative , Extrapolation method