The modified simplest equation procedure for conformable time-fractional Boussinesq equations


Razzaq W., Zafar A., Akbulut A.

INTERNATIONAL JOURNAL OF MODERN PHYSICS B, vol.36, no.17, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 17
  • Publication Date: 2022
  • Doi Number: 10.1142/s0217979222500953
  • Journal Name: INTERNATIONAL JOURNAL OF MODERN PHYSICS B
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: The modified simplest equation procedure, conformable derivatives, fractional differential equation, traveling wave transformation, exact solutions, PARTIAL-DIFFERENTIAL-EQUATIONS, TRAVELING-WAVE SOLUTIONS, FUNCTIONAL VARIABLE METHOD, FORNBERG-WHITHAM EQUATION, SOLITARY WAVE, NONLINEAR-WAVES, KLEIN-GORDON, SOLITONS, ORDER, TRANSFORM

Abstract

In this paper, we used the traveling wave transformation to find out the exact solutions of the conformable time fractional differential equations with the help of the Modified simplest equation procedure. We applied the given procedure to two different equations which are conformable time-fractional Boussinesq and coupled Boussinesq equations. First, we reduced the given equations to ordinary differential equations using wave transformations. Then, we applied the procedure to the given equations. We obtained hyperbolic, trigonometric and rational solutions. We gave the 3D plots, 2D plots and contour plots for some obtained solutions. According to our results, we can say the given method is effective, powerful and gives simple, reliable solutions compared to the other methods. All obtained solutions were checked with the help of Mathematica.