• Analytical solutions of time–space fractional, advection–dispersion andWhitham–Broer–Kaup equations

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      https://www.ias.ac.in/article/fulltext/pram/083/06/0885-0906

    • Keywords

       

      Modified Riemann–Liouville fractional derivative; Lie symmetries, optimal system; invariant solutions.

    • Abstract

       

      In this article, we study time–space fractional advection–dispersion (FADE) equation and time–space fractional Whitham–Broer–Kaup (FWBK) equation that have significant roles in hydrology. We introduce suitable transformations to convert fractional-order derivatives to integerorder derivatives and as a result these equations transform into partial differential equations (PDEs). Then the Lie symmetries and the corresponding optimal systems of the resulting PDEs are derived. The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional differential equations.

    • Author Affiliations

       

      M D Khan1 I Naeem1 M Imran2

      1. Department of Mathematics, School of Science and Engineering, Lahore University of Management Sciences, Lahore Cantt 54792, Pakistan
      2. Department of Mathematics & Natural Sciences, Gulf University for Science & Technology, Kuwait
    • Dates

       
  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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