IJPAM: Volume 78, No. 2 (2012)

ANALYTICAL APPROXIMATE SOLUTION TO
THE TIME-SPACE NONLINEAR PARTIAL
FRACTIONAL DIFFERENTIAL EQUATIONS

Kamal M. Hemida$^1$, Khaled A. Gepreel$^2$, Mohamed S. Mohamed$^3$
$^{1,3}$Mathematics Department
Faculty of Science
Al-Azhar University
Nasr City, 11884, Cairo, EGYPT
$^2$Mathematics Department
Faculty of Science
Zagazig University
Zagazig, EGYPT
$^{2,3}$Mathematics Department
Faculty of Science
Taif University
Taif, SAUDI ARABIA


Abstract. The fractional derivatives in the sense of Caputo, and the Homotopy analysis method HAM are used to construct approximate solutions for some nonlinear partial fractional differential equations via the fractional cubic nonlinear Schrodinger equation. The numerical results show that the approaches are easy to implement and accurate when applied to space-time fractional cubic nonlinear fractional equation. The methods introduce a promising tool for solving many space-time fractional partial differential equations. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equation.

Received: March 17, 2012

AMS Subject Classification: 14F35, 26A33, 34A08

Key Words and Phrases: Homotopy analysis method, fractional cubic nonlinear equation, Caputo derivative

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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: 78
Issue: 2