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Computing wave solutions and conservation laws of conformable time-fractional Gardner and Benjamin–Ono equations

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Abstract

This paper presents travelling wave solutions for the nonlinear time-fractional Gardner and Benjamin–Ono equations via the exp(\(- \Phi ( \varepsilon ))\)-expansion approach. Specifically, both the models are studied in the sense of conformable fractional derivative. The obtained travelling wave solutions are structured in rational, trigonometric (periodic solutions) and hyperbolic functions. Further, the investigation of symmetry analysis and nonlinear self-adjointness for the governing equations are discussed. The exact derived solutions could be very significant in elaborating physical aspects of real-world phenomena. We have 2D and 3D illustrations for free choices of the physical parameter to understand the physical explanation of the problems. Moreover, the underlying equations with conformable derivative have been investigated using the new conservation theorem.

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Acknowledgements

The authors are very grateful to the editor and the anonymous reviewer for providing valuable suggestions for the betterment of the manuscript. Sudhir Singh would like to thanks MHRD and National Institute of Technology, Tiruchirappalli, India for financial support through institute fellowship.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Tiruchirappalli , 620 015, India

    Sudhir Singh & K Murugesan

  2. Department of Applied Mathematics, Bharathiar University, Coimbatore , 641 046, India

    R Sakthivel

  3. Department of Mathematics, Science faculty, Firat University, 23119 , Elazig, Turkey

    M Inc

  4. Department of Computer Engineering, Biruni University, 34010 , Istanbul, Turkey

    A Yusuf

  5. Department of Mathematics, Science Faculty, Federal University Dutse, 7156 , Jigawa, Nigeria

    A Yusuf

Authors
  1. Sudhir Singh
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  2. R Sakthivel
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  3. M Inc
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  4. A Yusuf
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  5. K Murugesan
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Correspondence to R Sakthivel.

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Singh, S., Sakthivel, R., Inc, M. et al. Computing wave solutions and conservation laws of conformable time-fractional Gardner and Benjamin–Ono equations. Pramana - J Phys 95, 43 (2021). https://doi.org/10.1007/s12043-020-02070-0

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  • DOI: https://doi.org/10.1007/s12043-020-02070-0

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