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Solitary wave solutions for some nonlinear time-fractional partial differential equations

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Abstract

In this work, we have considered the Riccati–Bernoulli sub-ODE method for obtaining the exact solutions of nonlinear fractional-order differential equations. The fractional derivatives are described in Jumarie’s modified Riemann–Liouville sense. The space–time fractional modified equal width (mEW) equation and time-fractional generalised Hirota–Satsuma coupled Korteweg–de Vries (KdV) equations are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations (ODEs), which were obtained from the nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically.

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Acknowledgements

The authors thank the editor and anonymous reviewers for their useful comments and suggestions.

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Authors and Affiliations

  1. College of Science and Human Studies, Imam Abdulrahman Bin Faisal University, Jubail, Saudi Arabia

    S Z Hassan

  2. Department of Mathematics, Faculty of Science, Mansoura University, El Gomhouria St, Mansoura, Dakahlia Governorate , 35516, Egypt

    Mahmoud A E Abdelrahman

Authors
  1. S Z Hassan
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  2. Mahmoud A E Abdelrahman
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Correspondence to S Z Hassan.

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Hassan, S.Z., Abdelrahman, M.A.E. Solitary wave solutions for some nonlinear time-fractional partial differential equations. Pramana - J Phys 91, 67 (2018). https://doi.org/10.1007/s12043-018-1636-8

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  • DOI: https://doi.org/10.1007/s12043-018-1636-8

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