Skip to main content
SpringerLink
Log in

The modified simple equation method for solving some fractional-order nonlinear equations

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

Nonlinear fractional differential equations are encountered in various fields of mathematics, physics, chemistry, biology, engineering and in numerous other applications. Exact solutions of these equations play a crucial role in the proper understanding of the qualitative features of many phenomena and processes in various areas of natural science. Thus, many effective and powerful methods have been established and improved. In this study, we establish exact solutions of the time fractional biological population model equation and nonlinear fractional Klein–Gordon equation by using the modified simple equation method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2

Similar content being viewed by others

References

  1. K B Oldham and F Spanier, The fractional calculus (Academic Press, New York, 1974)

    MATH  Google Scholar 

  2. I Podlubny, Fractional differential equations (Academic Press, San Diego, 1999)

    MATH  Google Scholar 

  3. S G Samko, A A Kilbas and O I Marichev, Fractional integrals and derivatives theory and applications (Gordon and Breach, New York, 1993) p. 11

  4. K S Miller and B Ross, An introduction to the fractional calculus and fractional differential equations (Wiley, New York, 1993)

    MATH  Google Scholar 

  5. A A Kilbas, H M Srivastava and J J Trujillo, Theory and applications of fractional differential equations (Elsevier, Amsterdam, 2006)

    MATH  Google Scholar 

  6. A Carpinteri and F Mainardi, Fractals and fractional calculus in continuum mechanics (Springer, Wien, 1997)

    Book  MATH  Google Scholar 

  7. S Zhang, Q-A Zong, D Liu and Q Gao, Commun. Fractional Calculus 1(1), 48 (2010)

    Google Scholar 

  8. A Bekir, O Guner and A C Cevikel, Ab. Appl. Anal. 2013, 426462 (2013)

    MathSciNet  Google Scholar 

  9. N Shang and B Zheng, Int. J. Appl. Math. 3, 43 (2013)

    Google Scholar 

  10. B Zheng, Commun. Theor. Phys. 58, 623 (2012)

    Article  Google Scholar 

  11. B Lu, J. Math. Anal. Appl. 395, 684 (2012)

    Article  MathSciNet  Google Scholar 

  12. M Eslami, B F Vajargah, M Mirzazadeh and A Biswas, Indian J. Phys. 88(2), 177 (2014)

    Article  Google Scholar 

  13. B Tong, Y He, L Wei and X Zhang, Phys. Lett. A 376(3), 2588 (2012)

    Article  ADS  Google Scholar 

  14. J F Alzaidy, Brit. J. Math. Comput. Sci. 3, 153 (2013)

  15. W Liu and K Chen, Pramana – J. Phys. 81(3), 377 (2013)

    Article  ADS  Google Scholar 

  16. A C Cevikel, A Bekir, M Akar and S San, Pramana – J. Phys. 79(3), 337 (2012)

    Article  ADS  Google Scholar 

  17. N Taghizadeh, M Mirzazadeh, M Rahimian and M Akbari, Ain Shams Eng. J. 4, 897 (2013)

    Article  Google Scholar 

  18. Y Pandir, Y Gurefe and E Misirli, Int. J. Model Optim. 3(4), 349 (2013)

    Article  Google Scholar 

  19. Q Huang and R Zhdanov, Physica A 409, 110 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  20. M Caputo, J. Royal Astronom. Soc. 13, 529 (1967)

    Article  ADS  Google Scholar 

  21. G Jumarie, Comput. Math. Appl. 51, 1367 (2006)

    Article  MathSciNet  Google Scholar 

  22. G Jumarie, Appl. Math. Lett. 22, 378 (2009)

    Article  MathSciNet  Google Scholar 

  23. Z B Li and J H He, Math. Comput. Appl. 15, 970 (2010)

    MathSciNet  Google Scholar 

  24. J-H He and Z B Li, Therm. Sci. Math. Comput. 16(2), 331 (2012)

    Google Scholar 

  25. N Taghizadeh, M Mirzazadeh, A Samiei Paghaleh and J Vahidi, Ain Shams Eng. J. 3, 321 (2012)

    Article  Google Scholar 

  26. K Khan and M A Akbar, Ain Shams Eng. J. 4, 903 (2013)

    Article  Google Scholar 

  27. K Khan and M A Akbar, J. Assoc. Arab Univer. Basic Appl. Sci. 15, 74 (2014)

    Google Scholar 

  28. A M A El-Sayed, S Z Rida and A A M Arafa, Commun. Theor. Phys. (Beijing, China) 52, 992 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  29. S Zhang and H Q Zhang, Phys. Lett. A 375, 1069 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  30. N Taghizadeh, M Mirzazadeh, M Rahimian and M Akbari, Ain Shams Eng. J. 4, 897 (2013)

    Article  Google Scholar 

  31. B Lu, J. Math. Anal. Appl. 395, 684 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Art-Science Faculty, Department of Mathematics-Computer, Eskişehir Osmangazi University, Eskişehir, Turkey

    MELIKE KAPLAN & AHMET BEKIR

Authors
  1. MELIKE KAPLAN
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. AHMET BEKIR
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to MELIKE KAPLAN.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

KAPLAN, M., BEKIR, A. The modified simple equation method for solving some fractional-order nonlinear equations. Pramana - J Phys 87, 15 (2016). https://doi.org/10.1007/s12043-016-1205-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-016-1205-y

Keywords

PACS Nos

Search

Navigation