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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 276279, 10 pages
http://dx.doi.org/10.1155/2014/276279
Research Article

Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method

1Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan
2Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3Pioneer Center for Gifted Students, Ministry of Education, Jerash 26110, Jordan
4Applied Science Department, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan

Received 8 March 2014; Accepted 13 May 2014; Published 12 June 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 Shaher Momani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The multistep generalized differential transform method is applied to solve the fractional-order multiple chaotic FitzHugh-Nagumo (FHN) neurons model. The algorithm is illustrated by studying the dynamics of three coupled chaotic FHN neurons equations with different gap junctions under external electrical stimulation. The fractional derivatives are described in the Caputo sense. Furthermore, we present figurative comparisons between the proposed scheme and the classical fourth-order Runge-Kutta method to demonstrate the accuracy and applicability of this method. The graphical results reveal that only few terms are required to deduce the approximate solutions which are found to be accurate and efficient.