PL EN


Preferences help
enabled [disable] Abstract
Number of results
Journal
2013 | 11 | 10 | 1392-1398
Article title

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

Content
Title variants
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.
Publisher

Journal
Year
Volume
11
Issue
10
Pages
1392-1398
Physical description
Dates
published
1 - 10 - 2013
online
19 - 12 - 2013
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)
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0207-3
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.