Different methods for -dimensional space-time fractional modified KdV-Zakharov-Kuznetsov equation

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• 作者：Ozkan Guner^a ; ^{ozkanguner@karatekin.edu.tr" class="auth_mail" title="E-mail the corresponding author} ; Esin Aksoy^b ; ^{eesinaksoy@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Ahmet Bekir^c ; ^{abekir@ogu.edu.tr" class="auth_mail" title="E-mail the corresponding author} ; Adem C. Cevikel^b ; ^{acevikel@yildiz.edu.tr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Exp-function method ; (G&prime ; G)-expansion method ; Generalized Kudryashov method ; Modified Riemann&ndash ; Liouville derivative ; Space&ndash ; time fractional modified KdV&ndash ; Zakharov&ndash ; Kuznetsov equation
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：71
• 期：6
• 页码：1259-1269
• 全文大小：1195 K

文摘

In this paper, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the exp-function method, the class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116300463&_mathId=si14.gif&_user=111111111&_pii=S0898122116300463&_rdoc=1&_issn=08981221&md5=acbac6106e0a7bbeaf148403585b06db">class="imgLazyJSB inlineImage" height="31" width="29" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0898122116300463-si14.gif">class="mathContainer hidden">class="mathCode">$\left(\frac{G^{\prime }}{G}\right)$-expansion method and the generalized Kudryashov method are used to construct exact solutions for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116300463&_mathId=si13.gif&_user=111111111&_pii=S0898122116300463&_rdoc=1&_issn=08981221&md5=17c4fc12ba7963b63931d47b1844eaf6" title="Click to view the MathML source">(3+1)class="mathContainer hidden">class="mathCode">$(3+1)$-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation. This fractional equation can be turned into another nonlinear ordinary differential equation by fractional complex transformation and then these three methods are applied to solve it. As a result, some new exact solutions are obtained. The three methods demonstrate power, reliability and efficiency.