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The generalized Kudryashov method for nonlinear space–time fractional partial differential equations of Burgers type

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Abstract

The nonlinear space–time fractional differential equations (FDE) of Burgers’ type play an important role for describing many phenomena in applied sciences. This paper develops a generalized version of the modified Kudryashov method to obtain the exact solutions for FDE of Burgers’ type. The FDE are firstly reduced to a set of ordinary differential equations by means of a fractional complex transformation and, afterward, they are solved by applying the generalized Kudryashov method (GKM). Several kinds of traveling wave solutions such as kink and singular kink waves are illustrated with various figures and discussed. The results demonstrate the efficiency of the GKM in tackling space–time partial FDE.

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Acknowledgements

The authors would like to thank the deanship of scientific research of Majmaah University for the financial grant received for conducting this research (Project Number 68/38).

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Authors and Affiliations

  1. Department of Mathematics, College of Science and Humanities at Howtat Sudair, Majmaah University, Majmaah, 11952, Saudi Arabia

    A. A. Gaber

  2. Kingdom of Saudi Arabia Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk, 71491, Saudi Arabia

    A. F. Aljohani & A. Ebaid

  3. Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal

    J. Tenreiro Machado

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  1. A. A. Gaber
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  2. A. F. Aljohani
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  3. A. Ebaid
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  4. J. Tenreiro Machado
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Correspondence to A. Ebaid.

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The authors declare that they have no conflict of interest with regard to the publication of this manuscript. All authors contributed equally to this work.

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Gaber, A.A., Aljohani, A.F., Ebaid, A. et al. The generalized Kudryashov method for nonlinear space–time fractional partial differential equations of Burgers type. Nonlinear Dyn 95, 361–368 (2019). https://doi.org/10.1007/s11071-018-4568-4

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  • DOI: https://doi.org/10.1007/s11071-018-4568-4

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