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

      SUDHIR SINGH R SAKTHIVEL M INC A YUSUF K MURUGESAN

      Research Article Volume 95 Published: 25 February 2021 Article ID 0043

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/095/0043

    • Keywords

       

      Gardner equations; Benjamin–Ono equation; exp($-\Phi(\epsilon)$)-expansion approach; conformable fractional derivative; periodic solutions; symmetry analysis.

    • Abstract

       

      This paper presents travelling wave solutions for the nonlinear time-fractional Gardner and Benjamin–Ono equations via the exp($-\Phi(\epsilon)$)-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.

    • Author Affiliations

       

      SUDHIR SINGH1 R SAKTHIVEL2 M INC3 A YUSUF4 5 K MURUGESAN1

      1. Department of Mathematics, National Institute of Technology, Tiruchirappalli 620 015, India
      2. Department of Applied Mathematics, Bharathiar University, Coimbatore 641 046, India
      3. Department of Mathematics, Science faculty, Firat University, 23119 Elazig, Turkey
      4. Department of Computer Engineering, Biruni University, 34010 Istanbul, Turkey
      5. Department of Mathematics, Science Faculty, Federal University Dutse, 7156 Jigawa, Nigeria

    • Dates

       
      Published
      25 February 2021
      Manuscript received
      24 June 2020
      Manuscript revised
      26 September 2020
      Accepted
      4 November 2020
      Final version published online
      25 February 2021

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