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Traveling waves in rational expressions of exponential functions to the conformable time fractional Jimbo–Miwa and Zakharov–Kuznetsov equations

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Abstract

The conformable time fractional Jimbo–Miwa and Zakharov–Kuznetsov equations are solved by the generalized form of the Kudryashov method. A simple compatible wave transformation is employed to reduce the dimension of the equations to one. The predicted solution is of the form of a rational expression of two finite series at both the numerator and the denominator. The terms of both series are of the powers of some functions having exponential expressions satisfying a particular ODE. The exact solutions are expressed explicitly in terms of powers of some exponential functions in form of rational expressions.

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Acknowledgements

A part of this study was presented orally in International Congress on Fundamental and Applied Sciences 2017, Sarajevo, Bosnia and Herzegovina.

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Authors and Affiliations

  1. Department of Mathematics, Çankırı Karatekin University, 18200, Çankırı, Turkey

    Alper Korkmaz

  2. Department of Mathematics and Computer, Eskişehir Osmangazi University, 26040, Eskisehir, Turkey

    Ozlem Ersoy Hepson

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  1. Alper Korkmaz
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  2. Ozlem Ersoy Hepson
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Correspondence to Alper Korkmaz.

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Korkmaz, A., Hepson, O.E. Traveling waves in rational expressions of exponential functions to the conformable time fractional Jimbo–Miwa and Zakharov–Kuznetsov equations. Opt Quant Electron 50, 42 (2018). https://doi.org/10.1007/s11082-017-1313-z

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  • DOI: https://doi.org/10.1007/s11082-017-1313-z

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