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Comparison of numerical results of Fornberg-Whitham equation via OAFM is compared with HPTM when α = 1.0

Comparison of numerical results of Fornberg-Whitham equation via OAFM is compared with HPTM when α = 1.0

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In this article, approximate solutions of some PDE of fractional order are investi­gated with the help of a new semi-analytical method called the optimal auxiliary function method. The proposed method was tested upon the time-fractional Fisher equation, the time-fractional Fornberg-Whitham equation, and the time-fractional Inviscid Burger equation....

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... It has significant implications for many fields of science and engineering, fluid mechanics, mathematical physics, mathematical biology, hydrodynamics, and many others [1][2][3][4][5][6][7]. Since NLEEs are very difficult to unravel, so many powerful analytical and numerical methods are developed and established for solutions such as the sine-Gordon technique [8], the improved F-expansion approach [9], the enhanced ( ′ G G / )-expansion method [10,11], the binary Darboux transformation [12], the variational direct method [13], the extended version of exp (−ψ κ ( ))-expansion method [14], the Hirota direct methodology [15], the Lie symmetry approach [16,17], the extended Kudryashov method [18], the extended homoclinic test technique [19], the ′ G G G / , 1/ ( )expansion approach [20], the meshless method [21], the Mohand variational transform method [22], the Paul-Painlevé approach method [23], the exact solution method [24], the optimal auxiliary function method [25], the extended simple equation technique [26], the Bernoulli sub-ordinary differential equation approach [27], the (w g / )-expansion method [28], the improved F-expansion and unified methods [29], and the modified version of the new Kudryashov method [30]. ...
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