Projectile motion using three parameter Mittag-Leffler function calculus

Ahmed Bokhari, Rachid Belgacem, Sunil Kumar, Dumitru Baleanu and Salih Djilali

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 195, issue C, 22-30

Abstract: 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 Eα,βγ(z). We recover the cases when applying Caputo and ordinary derivatives.

Keywords: Projectile motion; Prabhakar derivative; Three Mittag-Leffler functions; Sumudu transform (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:195:y:2022:i:c:p:22-30

DOI: 10.1016/j.matcom.2021.12.020

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