The closed-form solution by the exponential rational function method for the nonlinear variable-order fractional differential equations

Mashael M. ALBaidani, Umair Ali, Abdul Hamid Ganie

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The symmetry features of fractional differential equations allow effective explanation of physical and biological phenomena in nature. The generalized form of the fractional differential equations is the variable-order fractional differential equations that describe the physical and biological applications. This paper discusses the closed-form traveling wave solutions for the nonlinear space–time variable-order fractional modified Kawahara and (2 + 1)-dimensional Burger hierarchy equations. The variable-order fractional differential equation has a derivative operator in the Caputo sense that is converted into the integer-order ordinary differential equation (ODE) by fractional transformation. The obtained ODE is solved by the exponential rational function method, and as a result, new exact solutions are constructed. Two problems are proposed to confirm the solutions of the space-time variable-order fractional differential equations.

Original languageEnglish
Article number1347636
JournalFrontiers in Physics
Volume12
DOIs
StatePublished - 2024

Keywords

  • closed-form traveling wave solution
  • exponential rational function method
  • variable-order Caputo derivative
  • variable-order fractional (2+1)-dimensional Burger hierarchy equation
  • variable-order fractional modified Kawahara equation

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