Variational iteration method - a promising technique for constructing equivalent integral equations of fractional order

• Authors: Yi-Hong Wang , Guo-Cheng Wu , Dumitru Baleanu
• Languages of publication: EN

Abstracts

EN

The variational iteration method is newly used to construct various integral equations of fractional order. Some iterative schemes are proposed which fully use the method and the predictor-corrector approach. The fractional Bagley-Torvik equation is then illustrated as an example of multi-order and the results show the efficiency of the variational iteration method’s new role.

Keywords

EN

fractional differential equations; variational iteration method; predictor-corrector; symbolic computation

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 10
• Pages: 1392-1398

Dates

published

1 - 10 - 2013

online

19 - 12 - 2013

Contributors

author

Yi-Hong Wang

author

Guo-Cheng Wu

author

Dumitru Baleanu

References

• [1] K. Diethelm, N. J. Ford, Appl. Math. Comput. 154, 621 (2004) http://dx.doi.org/10.1016/S0096-3003(03)00739-2[Crossref]
• [2] F. W. Liu, V. Anh, I. Turner, J. Comput. Appl. Math. 166, 209 (2004) http://dx.doi.org/10.1016/j.cam.2003.09.028[Crossref]
• [3] C. Tadjeran, M. M. Meerschaert, H. P. Scheffler, J. Comput. Phys. 213, 205 (2006) http://dx.doi.org/10.1016/j.jcp.2005.08.008[Crossref]
• [4] W. H. Deng, J. Comput. Phys. 227, 1510 (2007) http://dx.doi.org/10.1016/j.jcp.2007.09.015[Crossref]
• [5] X. J. Li, C. J. Xu, SIAM J. Numer. Anal. 47, 2108 (2009) http://dx.doi.org/10.1137/080718942[Crossref]
• [6] C. P. Li, F. H. Zeng, Int. J. Bifur. Chao. 22, 1230014 (2012) http://dx.doi.org/10.1142/S0218127412300145[Crossref]
• [7] H. G. Sun, W. Chen, Y. Q. Chen, Physica A 388, 4586 (2009) http://dx.doi.org/10.1016/j.physa.2009.07.024[Crossref]
• [8] N. T. Shawagfeh, Appl. Math. Comput. 131, 517 (2002) http://dx.doi.org/10.1016/S0096-3003(01)00167-9[Crossref]
• [9] H. Jafari, V. Daftardar-Gejji, Appl. Math. Comput. 180, 488 (2006) http://dx.doi.org/10.1016/j.amc.2005.12.031[Crossref]
• [10] J. S. Duan, R. Rach, D. Baleanu, A. M. Wazwaz, Commun. Frac. Calc. 3, 73 (2012)
• [11] Q. Wang, Chaos, Soliton. Fractal. 35, 843 (2008) http://dx.doi.org/10.1016/j.chaos.2006.05.074[Crossref]
• [12] S. Momani, Z. Odibat, Phys. Lett. A 365, 345 (2007) http://dx.doi.org/10.1016/j.physleta.2007.01.046[Crossref]
• [13] J. H. He, Comput. Meth. Appl. Mech. Engr. 167, 57 (1998) http://dx.doi.org/10.1016/S0045-7825(98)00108-X[Crossref]
• [14] G. C. Wu, D. Baleanu, Appl. Math. Model. 37, 6183 (2013) http://dx.doi.org/10.1016/j.apm.2012.12.018[Crossref]
• [15] I. Podlubny, Fractional Differential Equations (Academic Press, New York, 1999)
• [16] A. A. Kilbas, H. M. Srivastav, J. J. Trujillo, Theory and applications of fractional differential equations (Elsevier, New York, 2006)
• [17] D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional calculus models and numerical methods (World Scientific, Singapore, 2012)
• [18] G. C. Wu, D. Baleanu, Adv. Diff. Equa. 2013, 18 (2013) http://dx.doi.org/10.1186/1687-1847-2013-18[Crossref]
• [19] G. C. Wu, D. Baleanu, Adv. Diff. Equa. 2013, 21 (2013) http://dx.doi.org/10.1186/1687-1847-2013-21[Crossref]
• [20] J. H. He, Int. J. Mod. Phys. B 20, 1141 (2006) http://dx.doi.org/10.1142/S0217979206033796[Crossref]
• [21] J. H. He, Abstr. Appl. Anal. 2012, 916793 (2012)
• [22] A. Ghorbani, Comput. Meth. Appl. Mech. Engr. 197, 4173 (2007) http://dx.doi.org/10.1016/j.cma.2008.04.015[Crossref]
• [23] J. H. He, X. H. Wu, Comput. Math. Appl. 54, 881 (2007) http://dx.doi.org/10.1016/j.camwa.2006.12.083[Crossref]
• [24] J. H. He, J. Comput. Appl. Math. 207, 3 (2007) http://dx.doi.org/10.1016/j.cam.2006.07.009[Crossref]
• [25] S. A. Khuri, A. Sayfy, Appl. Math. Lett. 25, 2298 (2012) http://dx.doi.org/10.1016/j.aml.2012.06.020[Crossref]
• [26] H. Jafari, M. Saeidy, D. Baleanu, Cent. Eur. J. Phys. 10, 76 (2012) http://dx.doi.org/10.2478/s11534-011-0083-7[Crossref]
• [27] H. Jafari, C. M. Khalique, Commun. Frac. Calc. 3, 38 (2012)
• [28] K. Diethelm, The Analysis of Fractional Differential Equations (Springer-Verlag, New York, 2004)

Identifiers

DOI

10.2478/s11534-013-0207-3