APPROXIMATE ANALYTICAL AND NUMERICAL
SOLUTIONS TO FRACTIONAL NEWELL-WHITEHEAD
EQUATION BY FRACTIONAL COMPLEX TRANSFORM
Mohamed S. Mohamed$^{1,2}$, Faisal Al-Malki$^{2}$, Rabeaa Talib$^{2}$

$^1$Department of Mathematics
Taif University
Taif, SAUDI ARABIA
$^2$Department Mathematics
Al Azhar University
Nasr City, 11884, Cairo, EGYPT
Abstract. The aim of this paper is by using the fractional complex transform and the optimal homotopy analysis by method (OHAM) to find the analytical approximate solutions for time-space nonlinear partial fractional Newell-Whitehead equations. Fractional complex transformation is proposed to convert time-space nonlinear partial fractional differential Newell-Whitehead equation to nonlinear partial differential equations. Also, we use the optimal homotopy analysis method (OHAM) to the obtained nonlinear PFDEs. This optimal approach has general meaning and can be used to get the fast convergent series solution of the different type of nonlinear partial fractional differential equations. The results reveal that this method is very effective and powerful to obtain the approximate solutions.
AMS Subject classification: 60H30, 60H15, 35R60
Keywords and phrases: optimal homotopy analysis method (OHAM), fractional complex transform, fractional Newell-Whitehead equation


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DOI: 10.12732/ijam.v26i6.2

Volume: 26
Issue: 6
Year: 2013