• The ($G' /G, 1/G$)-expansion method for solving nonlinear space–time fractional differential equations

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      https://www.ias.ac.in/article/fulltext/pram/087/02/0017

    • Keywords

       

      Exact solution, modified Riemann--Liouville fractional derivative, space–time Cahn--Allen equation, space–time Klein--Gordon equation, ($G' /G, 1/G$) -expansion method

    • Abstract

       

      In this work, we present ($G' /G, 1/G$)-expansion method for solving fractional differential equations based on a fractional complex transform. We apply this method for solving space–time fractional Cahn--Allen equation and space--time fractional Klein–Gordon equation. The fractional derivatives are described in the sense of modified Riemann--Lioville. As a result of some exact solution in the form of hyperbolic, trigonometric and rational solutions are deduced. The obtained solutions may be used for explaining of some physical problems.The($G' /G, 1/G$)-expansion method has a wider applicability for nonlinear equations. We have verified all the obtained solutions with the aid of Maple.

    • Author Affiliations

       

      EMRULLAH YA¸SAR1 ILKER BURAK GIRESUNLU1

      1. Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059, Bursa, Turkey
    • Dates

       
  • Pramana – Journal of Physics | News

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