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2013 | 11 | 10 | 1523-1527
Tytuł artykułu

Homotopy analysis method for solving Abel differential equation of fractional order

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this study, the homotopy analysis method is used for solving the Abel differential equation with fractional order within the Caputo sense. Stabilityand convergence of the proposed approach is investigated. The numerical results demonstrate that the homotopy analysis method is accurate and readily implemented.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
10
Strony
1523-1527
Opis fizyczny
Daty
wydano
2013-10-01
online
2013-12-19
Twórcy
  • Department of Mathematics, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran, jafari@umz.ac.ir
  • Department of Mathematics, Faculty of Basic Sciences, University of Malayer, P.O. Box 65719-95863, Malayer, Iran, ksayehvand@iust.ac.ir
  • Department of Mathematics, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran, tajadodi@umz.ac.ir
Bibliografia
  • [1] S. Liao, Ph.D thesis, Shanghai Jiao Tong University (1992) [WoS]
  • [2] S. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method (Chapman & Hall/CRC Press, Boca Raton, 2003) http://dx.doi.org/10.1201/9780203491164[Crossref]
  • [3] O. Abdulaziz, A. S. Bataineh, I. Hashim, Journal of Applied Mathematics and Computing 33, 61 (2010) http://dx.doi.org/10.1007/s12190-009-0274-1[Crossref]
  • [4] S. Liao, Int. J. Nonlinear Mech. 30, 37180 (1995)
  • [5] S. Liao, Commun. Nonlinear Sci. 2, 95 (1997) http://dx.doi.org/10.1016/S1007-5704(97)90047-2[Crossref]
  • [6] H. Xu, S. Liao, X. C. You, Commun. Nonlinear Sci. 14, 1152 (2009) http://dx.doi.org/10.1016/j.cnsns.2008.04.008[Crossref]
  • [7] H. Jafari, S. Seifi, Commun. Nonlinear Sci. 14, 2006 (2009) http://dx.doi.org/10.1016/j.cnsns.2008.05.008[Crossref]
  • [8] K. B. Oldham, J. Spanier, The Fractional Calculus (Academic Press, Now York and London, 1974)
  • [9] I. Podlubny, Fractional Differential Equation (Academic Press, San Diego, 1999)
  • [10] I. Podlubny, Fract. Calculus Appl. Anal. 5, 367 (2002)
  • [11] S. G. Samko, A. A. Kilbas, O. Igorevich, Fractional Integrals and Derivatives, Theory and Applications (Gordon and Breach, Yverdon, 1993)
  • [12] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier Science, Amsterdam, 2006)
  • [13] D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional Calculus Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos (World Scientific, Boston 2012)
  • [14] J. G. Lu, G. Chen, Chaos Sol. Fract. 27, 685 (2006) http://dx.doi.org/10.1016/j.chaos.2005.04.037[Crossref]
  • [15] H. Jafari, S. Momani, Phys. Lett. A 370, 388 (2007) http://dx.doi.org/10.1016/j.physleta.2007.05.118[Crossref]
  • [16] H. Jafari, V. Daftardar-Gejji, J. Comput. Appl. Math. 196, 644 (2006) http://dx.doi.org/10.1016/j.cam.2005.10.017[Crossref]
  • [17] A. Carpinteri, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics (Springer, Berlin, 1997)
  • [18] E. Hilfer (Ed.), Applications of Fractional Calculus in Physics (World Scientific, Singapore, 2000)
  • [19] J. Sabatier, O. P. Agrawal, J. A. Tenreiro Machado (Springer, The Netherlands, 2007)
  • [20] V. Lakshmikantham, A. S. Vatsala, Nonlinear Anal. 69, 2677 (2008) http://dx.doi.org/10.1016/j.na.2007.08.042[Crossref]
  • [21] H. Weitzner, G. M. Zaslavsky, Commun. Nonlinear Sci. 8, 273 (2003) http://dx.doi.org/10.1016/S1007-5704(03)00049-2[Crossref]
  • [22] J. Gine, X. Santallusia, J. Math. Anal. Appl. 370, 187 (2010) http://dx.doi.org/10.1016/j.jmaa.2010.04.046[Crossref]
  • [23] H. Jafari, S. Das, H. Tajadodi, Journal of King Saud University Science 23, 151 (2010) http://dx.doi.org/10.1016/j.jksus.2010.06.023[Crossref]
  • [24] H. Jafari, N. Kadkhoda, H. Tajadodi, S. A. Hosseini Matikolai, Int. J. Nonlin. Sci. Num. 11, 271 (2010)
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0209-1
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