Projectile motion via Riemann-Liouville calculus

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• 作者：Bashir Ahmad (1)
  Hanan Batarfi (1)
  Juan J Nieto (1) (2)
  脫scar Otero-Zarraqui帽os (2)
  Wafa Shammakh (1)
  
  1. Department of Mathematics ; Faculty of Science ; King Abdulaziz University ; P.O. Box 80203 ; Jeddah ; 21589 ; Saudi Arabia
  2. Departamento de An谩lisis Matem谩tico ; Facultad de Matem谩ticas ; Universidad de Santiago de Compostela ; Santiago de Compostela ; 15782 ; Spain
  
• 关键词：70B05 ; 34A08 ; projectile motion ; fractional calculus ; Riemann ; Liouville derivative ; Caputo derivative
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,588 KB
• 参考文献：1. Ebaid, A (2011) Analysis of projectile motion in view of fractional calculus. Appl. Math. Model. 35: pp. 1231-1239 CrossRef
  2. Kilbas, A, Srivastava, HM, Trujillo, JJ (2006) Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam CrossRef
  3. Samko, SG, Kilbas, AA, Marichev, OI (1993) Fractional Integrals and Derivatives: Theory and Applications. Gordon & Breach, Linghome
  4. Podlubny, I (1999) Fractional Differential Equations. Academic Press, San Diego
  5. Baleanu, D, Guvenc, ZB, Machado, JAT (2010) New Trends in Nanotechnology and Fractional Calculus Applications. Springer, New York 978-90-481-3293-5" target="_blank" title="It opens in new window">CrossRef
  6. Baleanu, D, Golmankhaneh, AK, Nigmatullin, R, Golmankhaneh, AK (2010) Fractional Newtonian mechanics. Cent. Eur. J.聽Phys. 8: pp. 120-125 9-0085-x" target="_blank" title="It opens in new window">CrossRef
  7. Golmankhaneh, AK, Yengejeh, AM, Baleanu, D (2012) On the fractional Hamilton and Lagrange mechanics. Int. J. Theor. Phys. 51: pp. 2909-2916 9-8" target="_blank" title="It opens in new window">CrossRef
  8. Rosales Garcia, JJ, Guia Calderon, M, Martinez Ortiz, J, Baleanu, D (2013) Motion of a particle in a resisting medium using fractional calculus approach. Proc. Rom. Acad., Ser. A 14: pp. 42-47
  9. Rosales, JJ, Guia, M, Gomez, F, Aguilar, F, Martinez, J (2014) Two dimensional fractional projectile motion in a resisting medium. Cent. Eur. J. Phys. 12: pp. 517-520 CrossRef
  10. Belmekki, M, Nieto, JJ, Rodr铆guez-L贸pez, R (2009) Existence of periodic solution for a nonlinear fractional differential equation. Bound. Value Probl. 2009: 9/324561" target="_blank" title="It opens in new window">CrossRef
  11. Baleanu, D, Diethelm, K, Scalas, E, Trujillo, JJ (2012) Fractional Calculus Models and Numerical Methods. World Scientific, Boston
  12. Priya, GS, Prakash, P, Nieto, JJ, Kayar, Z (2013) Higher-order numerical scheme for fractional heat equation with Dirichlet and Neumann boundary conditions. Numer. Heat Transf., Part B, Fundam. 63: pp. 540-559 90.2013.778719" target="_blank" title="It opens in new window">CrossRef
  13. Yang, XJ (2012) Advanced Local Fractional Calculus and Its Applications. World Science Publisher, New York
  14. Hayen, JC (2003) Projectile motion in a resistant medium. Part 1: exact solution and properties. Int. J. Non-Linear Mech. 38: pp. 357-369 CrossRef
  15. Hayen, JC (2003) Projectile motion in a resistant medium. Part 2: approximate solution and estimates. Int. J. Non-Linear Mech. 38: pp. 371-380 CrossRef
  
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

We present an analysis of projectile motion in view of fractional calculus. We obtain the solution for the problem using the Riemann-Liouville derivative, and then we compute some features of projectile motion in the framework of Riemann-Liouville fractional calculus. We compare the solutions using Caputo derivatives and Riemann-Liouville derivatives.