Projectile motion using three parameter Mittag-Leffler function calculus

In the present work, we study the motion of the projectile using the regularized Prabhakar derivative of order β. The correlation of physical quantities with units of measurement creates an obstacle in solving some fractional differential equations, as the solutions presented mathematically may not have a physical meaning. To overcome this problem and maintain dimensions of physical quantities, an auxiliary parameter σ is usually used. We obtain analytical solutions of the velocity fractional differential system in terms of the three parameters Mittag-Leffler function denoted E_α,β^γ(z). We recover the cases when applying Caputo and ordinary derivatives.