IJPAM: Volume 80, No. 5 (2012)

JACOBI ELLIPTIC NUMERICAL SOLUTIONS FOR
THE TIME FRACTIONAL DISPERSIVE
LONGWAVE EQUATION

Mohamed S. Mohamed$^1$, Faisal Al-Malki$^2$, Rabeaa Talib$^3$
$^{1,2}$Mathematics Department
Faculty of Science
Taif University
Hawia, 888 Taif, SAUDI ARABIA
$^{1,3}$Mathematics Department
Faculty of Science
Al-Azhar University
Nasr City, 11884, Cairo, EGYPT


Abstract. The fractional derivatives in the sense of Caputo, and the homotopy analysis method (HAM) are used to construct the approximate solutions for nonlinear fractional dispersive long wave equation with reaspect to time fractional derivative. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution.

Received: May 27, 2012

AMS Subject Classification: homotopy analysis method, Caputo's fractional derivative, fractional dispersive long wave equation

Key Words and Phrases: 14F35, 26A33

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 5