NEW WAVE FORM SOLUTIONS OF TIME-FRACTIONAL GARDNER EQUATION VIA FRACTIONAL RICCATI EXPANSION METHOD

NEW WAVE FORM SOLUTIONS OF TIME-FRACTIONAL GARDNER EQUATION VIA FRACTIONAL RICCATI EXPANSION METHOD

B. Karaman

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Abstract

In this current paper, the fractional Riccati expansion method is proposed for obtaining the new exact solutions of the time-fractional Gardner equation. The fractional derivative is considered in the sense of Jumarie's modi ed Riemann-Liouville fractional derivative (JMRFD). A travelling wave transformation is  rstly utilized to convert the nonlinear fractional partial di erential equation (NFPDE) into a fractional ordinary di erential equation (FODE). Our main intention in this present paper is to indicate that the suggested method is appropriate to obtain the new exact solutions of fractional partial di erential equations. It can be said that the main advantage of the mentioned scheme is very simple and easy to apply. As a result, all the obtained results are presented in the paper.

Keywords

Time-fractional Gardner equation, Fractional Riccati expansion method, Ju- marie's modi ed Riemann-Liouville derivative, Mittag-Le er function.