Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 19, 2013

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

  • Hossein Jafari EMAIL logo , Haleh Tajadodi , Dumitru Baleanu , Abdulrahim Al-Zahrani , Yahia Alhamed and Adnan Zahid
From the journal Open Physics

Abstract

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.

[1] I. Podlubny, Fractional Differential Equation, (San Diego, Academic Press, 1999) Search in Google Scholar

[2] S. G. Samko, A. A. Kilbas, O. Igorevich, Fractional Integrals and Derivatives, Theory and Applications, (Yverdon, Gordon and Breach, 1993) Search in Google Scholar

[3] A. A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, (Amsterdam, Elsevier Science, 2006) Search in Google Scholar

[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) 10.1142/8180Search in Google Scholar

[5] R. Hirota, Phys. Rev. Lett. 27, 1192 (1971) http://dx.doi.org/10.1103/PhysRevLett.27.119210.1103/PhysRevLett.27.1192Search in Google Scholar

[6] M. R. Miurs, (Springer, Berlin, 1978) Search in Google Scholar

[7] C. T. Yan, Phys. Lett. A 224, 77 (1996) http://dx.doi.org/10.1016/S0375-9601(96)00770-010.1016/S0375-9601(96)00770-0Search in Google Scholar

[8] Z. S. Lü, H.Q. Zhang, Commun. Theor. Phys. 39, 405 (2003) 10.1088/0253-6102/39/4/405Search in Google Scholar

[9] V. Daftardar-Gejji, H. Jafari, J. Math. Anal. Appl. 301, 508 (2005) http://dx.doi.org/10.1016/j.jmaa.2004.07.03910.1016/j.jmaa.2004.07.039Search in Google Scholar

[10] H. Jafari, V. Daftardar-Gejji, Appl. Math. Comput. 181, 598 (2006) http://dx.doi.org/10.1016/j.amc.2005.12.04910.1016/j.amc.2005.12.049Search in Google Scholar

[11] H. Jafari, H. Tajadodi, International Journal of Differential Equations 2010, 764738 (2010) http://dx.doi.org/10.1155/2010/76473810.1155/2010/764738Search in Google Scholar

[12] H. Jafari, A. Kadem, D. Baleanu, T. Yilmaz, Rom. Rep. Phys. 64, 337 (2012) Search in Google Scholar

[13] H. Jafari, N. Kadkhoda, H. Tajadodi, S. A. Hosseini Matikolai, Int. J. Nonlin. Sci. Num. 11, 271 (2010) 10.1515/IJNSNS.2010.11.S1.271Search in Google Scholar

[14] H. Jafari, S. Das, H. Tajadodi, Journal of King Saud University Science 23, 151 (2011) http://dx.doi.org/10.1016/j.jksus.2010.06.02310.1016/j.jksus.2010.06.023Search in Google Scholar

[15] H. Jafari, M. Nazari, D. Baleanu, C.M. Khalique, Comput. Math. Appl. [In Press] (2012) Search in Google Scholar

[16] E. G. Fan, Y. Hon, Chaos Soliton. Fract. 15, 599 (2003) 10.1016/S0960-0779(02)00144-3Search in Google Scholar

[17] M. Wang, Phys. Lett. A 199, 169 (1995) http://dx.doi.org/10.1016/0375-9601(95)00092-H10.1016/0375-9601(95)00092-HSearch in Google Scholar

[18] S. Zhang, Q.A. Zong, D. Liu, Q. Gao, Commun. Fract. Calc. 1, 48 (2010) Search in Google Scholar

[19] Y. Zhou, M. Wang, Y. Wang, Phys. Lett. A 308, 31 (2003) http://dx.doi.org/10.1016/S0375-9601(02)01775-910.1016/S0375-9601(02)01775-9Search in Google Scholar

[20] H. Jafari, M. Ghorbani, C.M. Khalique, Abstr. Appl. Anal. 2012, 962789 (2012). Search in Google Scholar

[21] G. Jumarie, Comput. Math. Appl. 51, 1367 (2006) http://dx.doi.org/10.1016/j.camwa.2006.02.00110.1016/j.camwa.2006.02.001Search in Google Scholar

[22] G. Jumarie, Appl. Math. Lett. 23, 1444 (2010) http://dx.doi.org/10.1016/j.aml.2010.08.00110.1016/j.aml.2010.08.001Search in Google Scholar

[23] Y. C. Hon, E.G. Fan, Chaos Soliton. Fract. 19, 515 (2004) http://dx.doi.org/10.1016/S0960-0779(03)00099-710.1016/S0960-0779(03)00099-7Search in Google Scholar

[24] S. Zhang, H. Zhang, Phys. Lett. A 375, 1069 (2011) http://dx.doi.org/10.1016/j.physleta.2011.01.02910.1016/j.physleta.2011.01.029Search in Google Scholar

[25] B. Tian, Y.T. Gao, Z. Naturforsch. A 57, 39 (2002) 10.1515/zna-2002-9-1004Search in Google Scholar

[26] Elsayed M. E. Zayed, Appl. Math. Comput. 218, 3962 (2011) http://dx.doi.org/10.1016/j.amc.2011.09.02510.1016/j.amc.2011.09.025Search in Google Scholar

[27] Z. Lian, S.Y. Lou, Nonlinear Anal. 63, 1167 (2005) http://dx.doi.org/10.1016/j.na.2005.03.03610.1016/j.na.2005.03.036Search in Google Scholar

[28] Z. Yan, Chaos, MM Res. 22, 302 (2003) 10.18261/ISSN1504-310X-2003-03-09Search in Google Scholar

[29] S. Wang, X. Tang, S.Y. Lou, Chaos Soliton. Fract. 21, 231 (2004) http://dx.doi.org/10.1016/j.chaos.2003.10.01410.1016/j.chaos.2003.10.014Search in Google Scholar

[30] A. M. Wazwaz, Appl. Math. Comput. 188, 1205 (2007) http://dx.doi.org/10.1016/j.amc.2006.10.07510.1016/j.amc.2006.10.075Search in Google Scholar

[31] J. J. Kim, W.P. Hong, Z. Naturforsch. 59a, 721 (2004) 10.1515/zna-2004-1101Search in Google Scholar

Published Online: 2013-12-19
Published in Print: 2013-10-1

© 2013 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 26.4.2024 from https://www.degruyter.com/document/doi/10.2478/s11534-013-0203-7/html
Scroll to top button