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A new modification in the exponential rational function method for nonlinear fractional differential equations

  • Naveed Ahmed
  • Sadaf Bibi
  • Umar Khan
  • Syed Tauseef Mohyud-Din
Regular Article
  • 64 Downloads
Part of the following topical collections:
  1. Focus Point on Modelling Complex Real-World Problems with Fractal and New Trends of Fractional Differentiation

Abstract.

We have modified the traditional exponential rational function method (ERFM) and have used it to find the exact solutions of two different fractional partial differential equations, one is the time fractional Boussinesq equation and the other is the (2+1)-dimensional time fractional Zoomeron equation. In both the cases it is observed that the modified scheme provides more types of solutions than the traditional one. Moreover, a comparison of the recent solutions is made with some already existing solutions. We can confidently conclude that the modified scheme works better and provides more types of solutions with almost similar computational cost. Our generalized solutions include periodic, soliton-like, singular soliton and kink solutions. A graphical simulation of all types of solutions is provided and the correctness of the solution is verified by direct substitution. The extended version of the solutions is expected to provide more flexibility to scientists working in the relevant field to test their simulation data.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Naveed Ahmed
    • 1
  • Sadaf Bibi
    • 1
  • Umar Khan
    • 2
  • Syed Tauseef Mohyud-Din
    • 3
  1. 1.Department of Mathematics, Faculty of SciencesHITEC UniversityTaxila CanttPakistan
  2. 2.Department of MathematicsCOMSATS Institute of Information TechnologyAbbottabadPakistan
  3. 3.Center for Research (CFR)University of Islamabad (UoI)IslamabadPakistan

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