Displaying Projectile Motion with Nonlinear Air Resistance Using Caputo’s Definition

Displaying projectile in a resisting medium for two dimension have two forms; An Ordinary differential equation and a fractional differential equation describe its behavior. The two equations include a nonlinear term, which represents the effect of the air resistance on the motion of the projectile. The development of the Ordinary differential equations for all nonlinear cases is obtained using a developed technique that combines the linear operator Laplace transform and the Adomian decomposition method (ADM) to solve the nonlinear part. To discuss the behavior of the projectile motion we plot the obtained results for several values and study the effect of the order of the nonlinear term on the achievable maximum height. On the other hand, the effects of the proportional factor and the projected mass on the motion have been shown by substituting different values and in the equations of motion. In addition to the Laplace Decomposition Method (LDM), we use the Caputo definition of the fractional derivative to investigate the fractional form of the projectile motion equation. The results show that all the results obtained in the ordinary case may be obtained from the fractional case when α=1. Mathematics Subject Classification 70K25; 34K37; 44Axx