On the concept of exact solution for nonlinear differential equations of fractional‐order |
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Authors: | Ozkan Guner Ahmet Bekir |
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Institution: | 1. Department of International Trade Faculty of Economics and Administrative Sciences, Cankiri Karatekin University, Cankiri, Turkey;2. Department of Mathematics‐Computer, Art‐Science Faculty, Eskisehir Osmangazi University, Eskisehir, Turkey |
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Abstract: | In this article, the new exact travelling wave solutions of the nonlinear space‐time fractional Burger's, the nonlinear space‐time fractional Telegraph and the nonlinear space‐time fractional Fisher equations have been found. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into ordinary differential equations of integer order in the sense of the Jumarie's modified Riemann–Liouville derivative. The ‐expansion method is effective for constructing solutions to the nonlinear fractional equations, and it appears to be easier and more convenient by means of a symbolic computation system. Copyright © 2016 John Wiley & Sons, Ltd. |
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Keywords: | modified Riemann– Liouville derivative the nonlinear space‐time fractional Burger's equation the nonlinear space‐time fractional Telegraph equation the nonlinear space‐time fractional Fisher equation |
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