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

      S Z HASSAN MAHMOUD A E ABDELRAHMAN

      Research Article Volume 91 Issue 5 November 2018 Article ID 0067

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    • Keywords

       

      Nonlinear fractional differential equation; Riccati–Bernoulli sub-ODE method; fractional modified equal width equation; time-fractional Hirota–Satsuma coupled KdV system; solitary wave solutions; exact solution

    • 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’smodified Riemann–Liouville sense. The space–time fractional modified equal width (mEW) equation and timefractional 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.

    • Author Affiliations

       

      S Z HASSAN1 MAHMOUD A E ABDELRAHMAN2

      1. College of Science and Human Studies, Imam Abdulrahman Bin Faisal University, Jubail, Saudi Arabia
      2. Department of Mathematics, Faculty of Science, Mansoura University, El Gomhouria St, Mansoura, Dakahlia Governorate 35516, Egypt

    • Dates

       
      Published
      1 November 2018
      Manuscript received
      4 December 2017
      Manuscript revised
      24 February 2018
      Accepted
      4 April 2018
      Early published
      Unedited version published online
      Final version published online
      18 September 2018

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