Topological Methods in Nonlinear Analysis

Algorithms for nonlinear fractional partial differential equations: A selection of numerical methods

Shaher Momani, Zaid Odibat, and Ishak Hashim

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Abstract

Fractional order partial differential equations, as generalization of classical integer order partial differential equations, are increasingly used to model problems in fluid flow, finance and other areas of applications. In this paper we present a collection of numerical algorithms for the solution of nonlinear partial differential equations with space- and time-fractional derivatives. The fractional derivatives are considered in the Caputo sense. Two numerical examples are given to demonstrate the effectiveness of the present methods. Results show that the numerical schemes are very effective and convenient for solving nonlinear partial differential equations of fractional order.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 31, Number 2 (2008), 211-226.

Dates
First available in Project Euclid: 13 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1463150265

Mathematical Reviews number (MathSciNet)
MR2432079

Zentralblatt MATH identifier
1133.65116

Citation

Momani, Shaher; Odibat, Zaid; Hashim, Ishak. Algorithms for nonlinear fractional partial differential equations: A selection of numerical methods. Topol. Methods Nonlinear Anal. 31 (2008), no. 2, 211--226. https://projecteuclid.org/euclid.tmna/1463150265


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