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

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Hosseini K., Xu Y., Mayeli P., Bekir A., Yao P., Zhou Q., ...More

OPTOELECTRONICS AND ADVANCED MATERIALS-RAPID COMMUNICATIONS, vol.11, pp.423-429, 2017 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 11
• Publication Date: 2017
• Journal Name: OPTOELECTRONICS AND ADVANCED MATERIALS-RAPID COMMUNICATIONS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.423-429
• Eskisehir Osmangazi University Affiliated: Yes

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(- phi(epsilon))-expansion method. Various families of solutions, such as the hyperbolic and trigonometric function solutions are formally achieved. Results reveal that the exp(- phi(epsilon))-expansion method is an efficient tool to derive the exact solutions of nonlinear fractional differential equations.