Motion of a particle in a resisting medium using fractional calculus approach

Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science

Volumn 14, Issue 1, 2013, Pages 42-47

  Garcia, J Juan Rosales ^a   Calderon, M Guia ^a   Ortiz, Juan Martinez ^b   Baleanu, Dumitru ^c,d,e  

^a UNIVERSITY OF GUANAJUATO   (Mexico)

^b UNIVERSIDAD AUTÓNOMA DE ZACATECAS   (Mexico)

^c KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^d CANKAYA UNIVERSITY   (Turkey)

^e INSTITUTE OF SPACE SCIENCES   (Romania)

Author keywords

Fractional calculus; Resisting medium; Vertical motion

Indexed keywords

EID: 84878389137     PISSN: 14549069     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

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.
4. V. KULISH, L. L. JOSE, Application of fractional calculus to fluid mechanics, Journal of Fluids Engineering, 124, 3, article 803, Article ID 147806, 2002.
5. K. OLDHAM, Fractional differential equations, in electrochemistry, Advances in Engineering software, 41, pp. 9-12, 2010.
6. D. BALEANU, K. DIETHELM, E. SCALAS, AND J. J. TRUJILLO, Fractional Calculus Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos, World Scientific, 2012.
7. M. CAPUTO, F. MAINARDI, A new dissipation model based on memory mechanism, Pure and Applied Geophysics, 91, 8, pp. 134-147, 1971.
8. S. WESTERLUND, Causality, Report No. 940426, University of Kalmar, 1994.
9. R.R. NIGMATULLIN, A.A. ARBUZOV, F. SALEHLI, A. GIZ, I. BAYRAK, H. CATALGIL-GIZ, The first experimental confirmation of the fractional kinetics containing the complex-power exponents: dielectric measurements of polymerization reactions, Physica B, 388, pp. 418-434, 2007
10. D. BALEANU, Z.B. GÜVENC, J.A TENREIRO MACHADO. New Trends in Nanotechnology and Fractional Calculus Applications. Springer, 2010.
11. S.F. KWOK, A falling body problem through the air in view of the fractional derivative approach, Physica A, 350, pp. 199-206, 2005.
12. E. ABDELHALIM, Analysis of projectile motion in view of fractional calculus, Applied Mathematical Modelling, 35, pp. 1231-1239, 2011.
13. J.F. GOMEZ-AGUILAR, J.J. ROSALES-GARCIA, J.J. BERNAL-ALVARADO, T. CORDOVA-FRAGA, R. GUZMAN-CABRERA, Fractional Mechanical Oscillator, Rev. Mex. Fs., 58, pp. 348-352, 2012.
14. S.T. THORNTON, J.B. MARION, Classical Dynamics of Particles and Systems. Ed. Thomson Brooks/Cole, 2004.
15. C.A. MONJE, Y.Q. CHEN, B.M. VINAGRE, D. XUE, V. FELIU, Fractional-Order Systems and Controls: Fundamentals and Applications, Springer-Verlag, London Limited, 2010.
16. A.K. GOLMANKHANEH, A.M. YENGEJEH, D. BALEANU, On the Fractional Hamilton and Lagrange Mechanics, International Journal of Theoretical Physics, 51, 9, pp. 2909-2916, 2012.
17. A. BABAKHANI, D. BALEANU, Existence and uniqueness of solution for a class of nonlinear fractional order differential equations, Abstract and Applied Analysis, 2012, 632681, 2012.
18. A. BABAKHANI, D. BALEANU, R.KHANBABAIE, Hopf bifurcation for a class of fractional differential equations with delay, Nonlinear Dynamics, 69, 3, pp. 721-729, 2012.
19. A.K. GOLMANKHANEH, T. KHATUNI, N.A. PORGHOVEH, D. BALEANU, Comparison of iterative methods by solving nonlinear Sturm-Liouville, Burgers and Navier-Stokes equations, Central European Journal of Physics, 10, 4, pp. 966-976, 2012.
20. M.A.E. HERZALLAH, D. BALEANU, Fractional Euler-Lagrange equations revisited, Nonlinear Dynamics, 69, 3, pp. 977-982, 2012.
21. D. BALEANU, H. MOHAMMADI, SH. REZAPOUR, Positive solutions of an initial value problem for nonlinear fractional differential equations, Abstract and Applied Analysis, 2012, p. 837437, 2012.
22. S.K. ELAGAN, D. BALEANU, Set-valued fixed-point theorems for generalized contractive mappings on fuzzy metric spaces, Abstract and Applied Analysis, 2012, p. 832807, 2012.
23. A.K. GOLMANKHANEH, Ali K. GOLMANKHANEH, D. BALEANU, Homotopy perturbation method for solving a system of Schrödinger-Korteweg-de Vries equations, Rom. Rep. Phys., 63, pp. 609-623, 2011.
24. A. KADEM, D. BALEANU, On fractional coupled Whitham-Broer-Kaup equations, Rom. J. Phys., 56, pp. 629-635, 2011.
25. R. EID, S.I. MUSLIH, D. BALEANU, E. RABEI, Fractional dimensional harmonic oscillator, Rom. J. Phys., 56, pp. 323-331, 2011
26. D. BALEANU, S.I. MUSLIH, E.M. RABEI, A.K. GOLMANKHANEH, A.K. GOLMANKHANEH, On fractional Hamiltonian systems possessing first-class constraints within Caputo derivatives, Rom. Rep. Phys., 63, pp. 3-8, 2011.
27. S.I. MUSLIH, D. BALEANU, Mandelbrot scaling and parametrization invariant theories, Rom. Rep. Phys., 62, pp. 689-696, 2010.
28. S.I. MUSLIH, M. SADDALLAH, D. BALEANU, E. RABEI, Lagrangian formulation of Maxwell's field in fractional D dimensional space-time, Rom. J. Phys, 55, pp. 659-663, 2010.
29. M.A.E. HERZALLAH, A.M.A. El-SAYED, D. BALEANU, On the fractional-order diffusion-wave process, Rom. J. Phys., 55, pp. 274-284, 2010.