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2014 | 12 | 7 | 517-520

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Two dimensional fractional projectile motion in a resisting medium


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In this paper we propose a fractional differential equation describing the behavior of a two dimensional projectile in a resisting medium. In order to maintain the dimensionality of the physical quantities in the system, an auxiliary parameter k was introduced in the derivative operator. This parameter has a dimension of inverse of seconds (sec)−1 and characterizes the existence of fractional time components in the given system. It will be shown that the trajectories of the projectile at different values of γ and different fixed values of velocity v
0 and angle θ, in the fractional approach, are always less than the classical one, unlike the results obtained in other studies. All the results obtained in the ordinary case may be obtained from the fractional case when γ = 1.










Physical description


1 - 7 - 2014
21 - 6 - 2014


  • Department of Electrical Engineering, DICIS, University of Gto, Campus Irapuato-Salamanca, Salamanca Gto, Mexico
  • Department of Electrical Engineering, DICIS, University of Gto, Campus Irapuato-Salamanca, Salamanca Gto, Mexico
  • Department of Solar Materials. Renewable Energy Institute, National Autonomous University of Mexico, Priv. Xochicalco s/n. Col. Centro, Temixco Morelos, Mexico
  • Academic Unit of Mathematics, Autonomous University of Zacatecas, Zacatecas, Mexico
  • Academic Unit of Mathematics, Autonomous University of Zacatecas, Zacatecas, Mexico


  • [1] K. Oldham, J. Spanier, The Fractional Calculus, (Academic Press, New York, 1974)
  • [2] I. Podlubny, Fractional Differential Equations, (Academic Press, New York, 1999)
  • [3] R. Hilfer, Applications of Fractional Calculus in Physics, (World Scientific, Singapore, 2000) http://dx.doi.org/10.1142/9789812817747[Crossref]
  • [4] S. G. Samko, A. A. Kilbas, O. I. Maritchev, Fractional Integrals and Derivatives, Theory and Applications, (Gordon and Breach Science Publishers, Langhorne, PA, 1993)
  • [5] M. Caputo, F. Mainardi, Pure Appl. Geophys. 91, 8 (1971) http://dx.doi.org/10.1007/BF00879562[Crossref]
  • [6] S. Westerlund. Causality, report no. 940426, University of Kalmar, (1994)
  • [7] R.R. Nigmatullin, A.A. Arbuzov, F. Salehli, A. Giz, I. Bayrak, H. Catalgil-Giz, Physica. B388 (2007)
  • [8] R.L. Magin, O. Abdullah, D. Baleanu, X. Joe Zhou, Journal of Magnetic Resonance, 190 (2008)
  • [9] V. Uchaikin, Fractional Derivatives for Physicists and Engineers, (Springer, 2013) http://dx.doi.org/10.1007/978-3-642-33911-0[Crossref]
  • [10] R.L. Magin, Fractional Calculus in Bioengineering, (Redding, CT: Begell House, 2006)
  • [11] C. M. Ionescu, R. De Keyser, IEEE Tans. Biomed. Eng. 56, 4 (2009) http://dx.doi.org/10.1109/TBME.2009.2037199[Crossref]
  • [12] R. Martin, J. J. Quintana, A. Ramos, L. De la Nuez, Proc. IEEE Conf. Electroche. (2008)
  • [13] I. S. Jesus, T. J. A. Machado, B. J. Cunha, J. Vibrations Control. 14, 9 (2008)
  • [14] D. Baleanu, Alireza K. Golmankhaneh, R. Nigmatullin, Ali K. Golmankhaneh, Cent. Eur. J. Phys. 8, 120 (2010) http://dx.doi.org/10.2478/s11534-009-0085-x[Crossref]
  • [15] A.K. Golmankhaneh, A.M. Yengejeh, D. Baleanu, Int. J. Theor. Phys. 51, 2909 (2012) http://dx.doi.org/10.1007/s10773-012-1169-8[Crossref]
  • [16] V. Kulish, L. L. José, Journal of Fluids Engineering 124, Article ID (2002)
  • [17] Baleanu D., Günvenc Z.B., Tenreiro Machado J.A. New Trends in Nanotechnology and Fractional Calculus Applications, (Springer, 2010) http://dx.doi.org/10.1007/978-90-481-3293-5[Crossref]
  • [18] D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo. Fractional Calculus Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos, (World Scientific, 2012)
  • [19] K. Diethelm. The Analysis of Fractional Differential Equations, (Springer-Verlag Berlin Heidelber, 2010) http://dx.doi.org/10.1007/978-3-642-14574-2[Crossref]
  • [20] Alireza, K. Golmankhaneh. Investigations in Dynamics: With Focus on Fractional Dynamics. (LAP Lambert, Academic Publishing, Germany, 2012)
  • [21] S. F. Kwok, Physica A 350, (2005)
  • [22] E. Abdelhalim, Applied Mathematical Modeling 35, (2011)
  • [23] J. F. Gómez-Aguilar, J. J. Rosales-García, J. J. Bernal-Alvarado, T. Córdova-Fraga, R. Guzmán-Cabrera, Rev. Mex. Fís. 58, (2012)
  • [24] J. J. Rosales, M. Guía, J. F. Gómez, V. I. Tkach, Discontinuity Nonlinearity and Complexity 1, 4 (2012)
  • [25] J. Juan Rosales García, M. Guía Calderon, Juan Martínez Ortiz, Dumitru Baleanu, Proceedings of the Romanian Academy, Serie A, 14, 1 (2013)
  • [26] S.T. Thornton, J.B. Marion. Classical Dynamics of Particles and Systems, (Ed. Thomson Brooks/cole, 2004)

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