Fractional sub-equation method for the fractional generalized reaction Duffing model and nonlinear fractional Sharma-Tasso-Olver equation

• Authors: Hossein Jafari , Haleh Tajadodi , Dumitru Baleanu , Abdulrahim Al-Zahrani , Yahia Alhamed , Adnan Zahid
• Languages of publication: EN

Abstracts

EN

In this paper the fractional sub-equation method is used to construct exact solutions of the fractional generalized reaction Duffing model and nonlinear fractional Sharma-Tasso-Olver equation.The fractional derivative is described in the Jumarie’s modified Riemann-Liouville sense. Two illustrative examples are given, showing the accuracy and convenience of the method.

Keywords

EN

fractional sub-equation method; fractional partial differential equation; fractional generalized reaction Duffing model; nonlinear fractional Sharma-Tasso-Olver equation

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 10
• Pages: 1482-1486

Dates

published

1 - 10 - 2013

online

19 - 12 - 2013

Contributors

author

Hossein Jafari

• Department of Mathematics, University of Mazandaran, P.O. Box 47416-95797, Babolsar, Iran

author

Haleh Tajadodi

• Department of Mathematics, University of Mazandaran, P.O. Box 47416-95797, Babolsar, Iran

author

Dumitru Baleanu

author

Abdulrahim Al-Zahrani

• Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box: 80204, Jeddah, 21589, Saudi Arabia

author

Yahia Alhamed

• Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box: 80204, Jeddah, 21589, Saudi Arabia

author

Adnan Zahid

• Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box: 80204, Jeddah, 21589, Saudi Arabia

References

• [1] I. Podlubny, Fractional Differential Equation, (San Diego, Academic Press, 1999)
• [2] S. G. Samko, A. A. Kilbas, O. Igorevich, Fractional Integrals and Derivatives, Theory and Applications, (Yverdon, Gordon and Breach, 1993)
• [3] A. A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, (Amsterdam, Elsevier Science, 2006)
• [4] D. Bǎleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos, (Boston, World Scientific, 2012)
• [5] R. Hirota, Phys. Rev. Lett. 27, 1192 (1971) http://dx.doi.org/10.1103/PhysRevLett.27.1192[Crossref]
• [6] M. R. Miurs, (Springer, Berlin, 1978)
• [7] C. T. Yan, Phys. Lett. A 224, 77 (1996) http://dx.doi.org/10.1016/S0375-9601(96)00770-0[Crossref]
• [8] Z. S. Lü, H.Q. Zhang, Commun. Theor. Phys. 39, 405 (2003)
• [9] V. Daftardar-Gejji, H. Jafari, J. Math. Anal. Appl. 301, 508 (2005) http://dx.doi.org/10.1016/j.jmaa.2004.07.039[Crossref]
• [10] H. Jafari, V. Daftardar-Gejji, Appl. Math. Comput. 181, 598 (2006) http://dx.doi.org/10.1016/j.amc.2005.12.049[Crossref]
• [11] H. Jafari, H. Tajadodi, International Journal of Differential Equations 2010, 764738 (2010) http://dx.doi.org/10.1155/2010/764738[Crossref]
• [12] H. Jafari, A. Kadem, D. Baleanu, T. Yilmaz, Rom. Rep. Phys. 64, 337 (2012)
• [13] H. Jafari, N. Kadkhoda, H. Tajadodi, S. A. Hosseini Matikolai, Int. J. Nonlin. Sci. Num. 11, 271 (2010)
• [14] H. Jafari, S. Das, H. Tajadodi, Journal of King Saud University Science 23, 151 (2011) http://dx.doi.org/10.1016/j.jksus.2010.06.023[Crossref]
• [15] H. Jafari, M. Nazari, D. Baleanu, C.M. Khalique, Comput. Math. Appl. [In Press] (2012)
• [16] E. G. Fan, Y. Hon, Chaos Soliton. Fract. 15, 599 (2003)
• [17] M. Wang, Phys. Lett. A 199, 169 (1995) http://dx.doi.org/10.1016/0375-9601(95)00092-H[Crossref]
• [18] S. Zhang, Q.A. Zong, D. Liu, Q. Gao, Commun. Fract. Calc. 1, 48 (2010)
• [19] Y. Zhou, M. Wang, Y. Wang, Phys. Lett. A 308, 31 (2003) http://dx.doi.org/10.1016/S0375-9601(02)01775-9[Crossref]
• [20] H. Jafari, M. Ghorbani, C.M. Khalique, Abstr. Appl. Anal. 2012, 962789 (2012).
• [21] G. Jumarie, Comput. Math. Appl. 51, 1367 (2006) http://dx.doi.org/10.1016/j.camwa.2006.02.001[Crossref]
• [22] G. Jumarie, Appl. Math. Lett. 23, 1444 (2010) http://dx.doi.org/10.1016/j.aml.2010.08.001[Crossref]
• [23] Y. C. Hon, E.G. Fan, Chaos Soliton. Fract. 19, 515 (2004) http://dx.doi.org/10.1016/S0960-0779(03)00099-7[Crossref]
• [24] S. Zhang, H. Zhang, Phys. Lett. A 375, 1069 (2011) http://dx.doi.org/10.1016/j.physleta.2011.01.029[Crossref]
• [25] B. Tian, Y.T. Gao, Z. Naturforsch. A 57, 39 (2002)
• [26] Elsayed M. E. Zayed, Appl. Math. Comput. 218, 3962 (2011) http://dx.doi.org/10.1016/j.amc.2011.09.025[Crossref]
• [27] Z. Lian, S.Y. Lou, Nonlinear Anal. 63, 1167 (2005) http://dx.doi.org/10.1016/j.na.2005.03.036[Crossref]
• [28] Z. Yan, Chaos, MM Res. 22, 302 (2003)
• [29] S. Wang, X. Tang, S.Y. Lou, Chaos Soliton. Fract. 21, 231 (2004) http://dx.doi.org/10.1016/j.chaos.2003.10.014[Crossref]
• [30] A. M. Wazwaz, Appl. Math. Comput. 188, 1205 (2007) http://dx.doi.org/10.1016/j.amc.2006.10.075[Crossref]
• [31] J. J. Kim, W.P. Hong, Z. Naturforsch. 59a, 721 (2004)

Identifiers

DOI

10.2478/s11534-013-0203-7