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

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Central European Journal of Physics

Abstract

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.

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References

  1. K. Diethelm, N. J. Ford, Appl. Math. Comput. 154, 621 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. F. W. Liu, V. Anh, I. Turner, J. Comput. Appl. Math. 166, 209 (2004)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  3. C. Tadjeran, M. M. Meerschaert, H. P. Scheffler, J. Comput. Phys. 213, 205 (2006)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  4. W. H. Deng, J. Comput. Phys. 227, 1510 (2007)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. X. J. Li, C. J. Xu, SIAM J. Numer. Anal. 47, 2108 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. C. P. Li, F. H. Zeng, Int. J. Bifur. Chao. 22, 1230014 (2012)

    Article  MathSciNet  Google Scholar 

  7. H. G. Sun, W. Chen, Y. Q. Chen, Physica A 388, 4586 (2009)

    Article  ADS  Google Scholar 

  8. N. T. Shawagfeh, Appl. Math. Comput. 131, 517 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. H. Jafari, V. Daftardar-Gejji, Appl. Math. Comput. 180, 488 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. J. S. Duan, R. Rach, D. Baleanu, A. M. Wazwaz, Commun. Frac. Calc. 3, 73 (2012)

    Google Scholar 

  11. Q. Wang, Chaos, Soliton. Fractal. 35, 843 (2008)

    Article  ADS  MATH  Google Scholar 

  12. S. Momani, Z. Odibat, Phys. Lett. A 365, 345 (2007)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  13. J. H. He, Comput. Meth. Appl. Mech. Engr. 167, 57 (1998)

    Article  ADS  MATH  Google Scholar 

  14. G. C. Wu, D. Baleanu, Appl. Math. Model. 37, 6183 (2013)

    Article  MathSciNet  Google Scholar 

  15. I. Podlubny, Fractional Differential Equations (Academic Press, New York, 1999)

    MATH  Google Scholar 

  16. A. A. Kilbas, H. M. Srivastav, J. J. Trujillo, Theory and applications of fractional differential equations (Elsevier, New York, 2006)

    MATH  Google Scholar 

  17. D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional calculus models and numerical methods (World Scientific, Singapore, 2012)

    MATH  Google Scholar 

  18. G. C. Wu, D. Baleanu, Adv. Diff. Equa. 2013, 18 (2013)

    Article  Google Scholar 

  19. G. C. Wu, D. Baleanu, Adv. Diff. Equa. 2013, 21 (2013)

    Article  Google Scholar 

  20. J. H. He, Int. J. Mod. Phys. B 20, 1141 (2006)

    Article  ADS  MATH  Google Scholar 

  21. J. H. He, Abstr. Appl. Anal. 2012, 916793 (2012)

    Google Scholar 

  22. A. Ghorbani, Comput. Meth. Appl. Mech. Engr. 197, 4173 (2007)

    Article  MathSciNet  Google Scholar 

  23. J. H. He, X. H. Wu, Comput. Math. Appl. 54, 881 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  24. J. H. He, J. Comput. Appl. Math. 207, 3 (2007)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  25. S. A. Khuri, A. Sayfy, Appl. Math. Lett. 25, 2298 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  26. H. Jafari, M. Saeidy, D. Baleanu, Cent. Eur. J. Phys. 10, 76 (2012)

    Article  Google Scholar 

  27. H. Jafari, C. M. Khalique, Commun. Frac. Calc. 3, 38 (2012)

    Google Scholar 

  28. K. Diethelm, The Analysis of Fractional Differential Equations (Springer-Verlag, New York, 2004)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Shanghai Normal University Tianhua College, Beijing, 201815, China

    Yi-Hong Wang

  2. Department of Mathematics, Zhejiang Forestry & Agriculture University, Linan, 311300, China

    Yi-Hong Wang

  3. College of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641112, China

    Guo-Cheng Wu

  4. College of Water Resources and Hydropower, Sichuan University, Chengdu, 610065, China

    Guo-Cheng Wu

  5. Department of Mathematics and Computer Sciences, Cankaya University, 06530, Balgat, Ankara, Turkey

    Dumitru Baleanu

  6. Institute of Space Sciences, Magurele-Bucharest, Romania

    Dumitru Baleanu

  7. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

    Dumitru Baleanu

Authors
  1. Yi-Hong Wang
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  2. Guo-Cheng Wu
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  3. Dumitru Baleanu
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Corresponding author

Correspondence to Guo-Cheng Wu.

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Wang, YH., Wu, GC. & Baleanu, D. Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order. centr.eur.j.phys. 11, 1392–1398 (2013). https://doi.org/10.2478/s11534-013-0207-3

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  • DOI: https://doi.org/10.2478/s11534-013-0207-3

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