Projectile motion using three parameter Mittag-Leffler function calculus

Abstract

In the present work, we study the motion of the projectile using the regularized Prabhakar derivative of order beta. 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 sigma is usually used. We obtain analytical solutions of the velocity fractional differential system in terms of the three parameters Mittag-Leffler function denoted Ea ,beta(z). We recover the cases when applying Caputo and ordinary derivatives. (c) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.