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Projectile motion using three parameter Mittag-Leffler function calculus

Author

Listed:
  • Bokhari, Ahmed
  • Belgacem, Rachid
  • Kumar, Sunil
  • Baleanu, Dumitru
  • Djilali, Salih

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.

Suggested Citation

  • Bokhari, Ahmed & Belgacem, Rachid & Kumar, Sunil & Baleanu, Dumitru & Djilali, Salih, 2022. "Projectile motion using three parameter Mittag-Leffler function calculus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 22-30.
    • Handle: RePEc:eee:matcom:v:195:y:2022:i:c:p:22-30
    DOI: 10.1016/j.matcom.2021.12.020
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    References listed on IDEAS

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    1. Fethi Bin Muhammed Belgacem & Ahmed Abdullatif Karaballi & Shyam L. Kalla, 2003. "Analytical investigations of the Sumudu transform and applications to integral production equations," Mathematical Problems in Engineering, Hindawi, vol. 2003, pages 1-16, January.
    2. Fethi Bin Muhammed Belgacem & Ahmed Abdullatif Karaballi, 2006. "Sumudu transform fundamental properties investigations and applications," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-23, May.
    3. Bentout, Soufiane & Djilali, Salih & Kumar, Sunil, 2021. "Mathematical analysis of the influence of prey escaping from prey herd on three species fractional predator-prey interaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
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