Skip to main content
Log in

The first integral method for Wu–Zhang system with conformable time-fractional derivative

  • Published:
Calcolo Aims and scope Submit manuscript

Abstract

In this paper, the first integral method is used to construct exact solutions of the time-fractional Wu–Zhang system. Fractional derivatives are described by conformable fractional derivative. This method is based on the ring theory of commutative algebra. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  1. Biswas, A., Bhrawy, A.H., Abdelkawy, M.A., Alshaery, A.A., Hilal, E.M.: Symbolic computation of some nonlinear fractional differential equations. Rom. J. Phys. 59(5–6), 0433–0442 (2014)

    Google Scholar 

  2. El-Sayed, A.M.A., El-Mesiry, A.E.M., El-Saka, H.A.A.: On the fractional-order logistic equation. Appl. Math. Lett. 20(7), 817–823 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ahmed, E., El-Sayed, A.M.A., El-Saka, H.A.: Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models. J. Math. Anal. Appl. 325(1), 542–553 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Laskin, N.: Fractional market dynamics. Phys. A: Stat. Mech. Appl. 287(3), 482–492 (2000)

    Article  MathSciNet  Google Scholar 

  5. Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)

    MATH  Google Scholar 

  6. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  7. Jumarie, G.: On the representation of fractional Brownian motion as an integral with respect to. Appl. Math. Lett. 18(7), 739–748 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jumarie, G.: Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Comput. Math. Appl. 51(9), 1367–1376 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu, C.S.: Counterexamples on Jumarie’s two basic fractional calculus formulae. Commun. Nonlinear Sci. Numer. Simul. 22(1), 92–94 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Khalil, R.: Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)

    Article  MathSciNet  Google Scholar 

  11. Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Feng, Z.: On explicit exact solutions to the compound Burgers-KdV equation. Phys. Lett. A 293(1), 57–66 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ding, T.R., Li, C.Z.: Ordinary Differential Equations. Peking University Press, Peking (1996)

    Google Scholar 

  14. Zheng, X., Chen, Y., Zhang, H.: Generalized extended tanh-function method and its application to (1+ 1)-dimensional dispersive long wave equation. Phys. Lett. A 311(2), 145–157 (2003)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers for their useful comments. This research work has been supported by a research grant from the University of Mazandaran.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mostafa Eslami.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eslami, M., Rezazadeh, H. The first integral method for Wu–Zhang system with conformable time-fractional derivative. Calcolo 53, 475–485 (2016). https://doi.org/10.1007/s10092-015-0158-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10092-015-0158-8

Keywords

Mathematics Subject Classification

Navigation