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Implementation of three reliable methods for finding the exact solutions of (2 + 1) dimensional generalized fractional evolution equations

  • Mostafa M. A. Khater
  • Dipankar Kumar
Article

Abstract

In this study, we have implemented the three methods namely extended \((G^{\prime}/G)\)-expansion, extended \((1/G^{\prime})\)-expansion and \((G^{\prime}/G,\,\,1/G)\)-expansion methods to determine exact solutions for the (2 + 1) dimensional generalized time–space fractional differential equations. We use Conformable fractional derivative and its properties in this research to convert fractional differential equations to ordinary differential equations with integer order. By using above mentioned methods, three types of traveling wave solutions are successfully obtained which have been expressed by the hyperbolic, trigonometric, and rational function solutions. The considered methods and transformation techniques are efficient and consistent for solving nonlinear time and space-fractional differential equations.

Keywords

(2 + 1) Dimensional generalized time–space fractional differential equations Extended \((G^{\prime}/G)\)-expansion method Extended \((1/G^{\prime})\)-expansion method The \((G^{\prime}/G,\,\,1/G)\)-expansion method Exact solutions 

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Copyright information

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Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceJiangsu UniversityZhenjiangChina
  2. 2.Department of Mathematics, Faculty of ScienceMansoura UniversityMansouraEgypt
  3. 3.Division of Engineering Mechanics and Energy, Graduate School of Systems and Information EngineeringUniversity of TsukubaTsukubaJapan
  4. 4.Department of MathematicsBangabandhu Sheikh Mujibur Rahman Science, and Technology UniversityGopalganjBangladesh

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