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Open AccessArticle

Fractional Whitham–Broer–Kaup Equations within Modified Analytical Approaches

1
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
2
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara 06530, Turkey
3
Institute of Space Sciences, 077125 Magurele, Romania
*
Author to whom correspondence should be addressed.
Axioms 2019, 8(4), 125; https://doi.org/10.3390/axioms8040125
Received: 12 October 2019 / Revised: 4 November 2019 / Accepted: 5 November 2019 / Published: 7 November 2019
The fractional traveling wave solution of important Whitham–Broer–Kaup equations was investigated by using the q-homotopy analysis transform method and natural decomposition method. The Caputo definition of fractional derivatives is used to describe the fractional operator. The obtained results, using the suggested methods are compared with each other as well as with the exact results of the problems. The comparison shows the best agreement of solutions with each other and with the exact solution as well. Moreover, the proposed methods are found to be accurate, effective, and straightforward while dealing with the fractional-order system of partial differential equations and therefore can be generalized to other fractional order complex problems from engineering and science. View Full-Text
Keywords: q-Homotopy analysis transform method; Natural decomposition method; Whitham–Broer–Kaup equations; Caputo derivative q-Homotopy analysis transform method; Natural decomposition method; Whitham–Broer–Kaup equations; Caputo derivative
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Shah, R.; Khan, H.; Baleanu, D. Fractional Whitham–Broer–Kaup Equations within Modified Analytical Approaches. Axioms 2019, 8, 125.

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