"

Cookies ussage consent

I agree.

Our site saves small pieces of text information (cookies) on your device in order to deliver better content and for statistical purposes. You can disable the usage of cookies by changing the settings of your browser. By browsing our site without changing the browser settings you grant us permission to store that information on your device.

A study on the conformable time-fractional Klein–Gordon equations with quadratic and cubic nonlinearities

K. HOSSEINI1, YUN-JIE XU2, P. MAYELI3, A. BEKIR4, PING YAO5, QIN ZHOU5,* , Ö. GÜNER6

Affiliation

  1. Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
  2. College of Engineering, Huzhou University, HuZhou, Zhejiang, 313000, P.R. China
  3. Young Researchers and Elite Club, Lahijan Branch, Islamic Azad University, Lahijan, Iran
  4. Department of Mathematics and Computer, Art –Science Faculty, Eskisehir Osmangazi University, Eskisehir, Turkey
  5. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan , 430212, P.R. China
  6. Department of International Trade, Faculty of Economics and Administrative Sciences, Cankiri Karatekin Uni versity, Cankiri, Turkey

Abstract

The nonlinear time-fractional Klein–Gordon equations are a class of fractional partial differential equations which are used for delineation of some physical phenomena in solid state physics, nonlinear optics, and quantum field theory. In this paper, the time-fractional Klein–Gordon equations with quadratic and cubic nonlinearities in the context of the conformable fractional derivative are explored via a recently developed approach named the exp   -expansion method. Various families of solutions, such as the hyperbolic and trigonometric function solutions are formally achieved. Results reveal that the exp-expansion method is an efficient tool to derive the exact solutions of nonlinear fractional differential equations..

Keywords

Time-fractional Klein–Gordon equations, Conformable fractional derivative, Quadratic and cubic nonlinearities, Exp-expansion method, Hyperbolic and trigonometric solutions.

Citation

K. HOSSEINI, YUN-JIE XU, P. MAYELI, A. BEKIR, PING YAO, QIN ZHOU, Ö. GÜNER, A study on the conformable time-fractional Klein–Gordon equations with quadratic and cubic nonlinearities, Optoelectronics and Advanced Materials - Rapid Communications, 11, 7-8, July-August 2017, pp.423-429 (2017).

Submitted at: Jan. 31, 2017

Accepted at: Aug. 9, 2017