Exact solutions of the space time-fractional Klein-Gordon equation with cubic nonlinearities using some methods


ÖZKAN A., ÖZKAN E. M.

COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, vol.10, no.3, pp.674-685, 2022 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.22034/cmde.2021.41121.1783
  • Journal Name: COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS
  • Journal Indexes: Emerging Sources Citation Index, Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.674-685
  • Keywords: Space time fractional Klein-Gordon equation, Ansatz method, Modified Kudryashov method, Exact solutions, DARK SOLITON-SOLUTIONS, DIFFERENTIAL-EQUATIONS, ZAKHAROV-KUZNETSOV, PERIODIC-SOLUTIONS, 1-SOLITON SOLUTION, OPTICAL SOLITONS, COUPLE, BRIGHT

Abstract

Recently, finding exact solutions of nonlinear fractional differential equations has attracted great interest. In this work, the space time-fractional Klein-Gordon equation with cubic nonlinearities is examined. Firstly, suitable exact soliton solutions are formally extracted by using the solitary wave ansatz method. Some solutions are also illustrated by the computer simulations. Besides, the modified Kudryashov method is used to construct exact solutions of this equation.