In this paper, we formulate a new nonstandard finite difference (NSFD) scheme to study the dynamic treatments of a class of fractional chaotic systems. To design the new proposed scheme, an appropriate nonlocal framework is applied for the discretization of nonlinear terms. This method is easy to implement and preserves some important physical properties of the considered model, e.g., fixed points and their stability. Additionally, this scheme is explicit and inexpensive to solve fractional differential equations (FDEs). From a practical point of view, the stability analysis and chaotic behavior of three novel fractional systems are provided by the proposed approach. Numerical simulations and comparative results confirm that this scheme is also successful for the fractional chaotic systems with delay arguments.
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February 2018
Research-Article
An Efficient Nonstandard Finite Difference Scheme for a Class of Fractional Chaotic Systems
Mojtaba Hajipour,
Mojtaba Hajipour
Department of Mathematics,
Sahand University of Technology,
Tabriz 5376138461, Iran
e-mail: hajipour@sut.ac.ir
Sahand University of Technology,
Tabriz 5376138461, Iran
e-mail: hajipour@sut.ac.ir
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Amin Jajarmi,
Amin Jajarmi
Department of Electrical Engineering,
University of Bojnord,
Bojnord 9453155111, Iran
e-mail: a.jajarmi@ub.ac.ir
University of Bojnord,
P.O. Box 94531-1339
,Bojnord 9453155111, Iran
e-mail: a.jajarmi@ub.ac.ir
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Dumitru Baleanu
Dumitru Baleanu
Department of Mathematics,
Faculty of Arts and Sciences,
Cankaya University,
Ankara 06530, Turkey;
Faculty of Arts and Sciences,
Cankaya University,
Ankara 06530, Turkey;
Institute of Space Sciences,
Magurele-Bucharest 76900, Romania
e-mail: dumitru@cankaya.edu.tr
P.O. Box, MG-23, R 76900
,Magurele-Bucharest 76900, Romania
e-mail: dumitru@cankaya.edu.tr
Search for other works by this author on:
Mojtaba Hajipour
Department of Mathematics,
Sahand University of Technology,
Tabriz 5376138461, Iran
e-mail: hajipour@sut.ac.ir
Sahand University of Technology,
Tabriz 5376138461, Iran
e-mail: hajipour@sut.ac.ir
Amin Jajarmi
Department of Electrical Engineering,
University of Bojnord,
Bojnord 9453155111, Iran
e-mail: a.jajarmi@ub.ac.ir
University of Bojnord,
P.O. Box 94531-1339
,Bojnord 9453155111, Iran
e-mail: a.jajarmi@ub.ac.ir
Dumitru Baleanu
Department of Mathematics,
Faculty of Arts and Sciences,
Cankaya University,
Ankara 06530, Turkey;
Faculty of Arts and Sciences,
Cankaya University,
Ankara 06530, Turkey;
Institute of Space Sciences,
Magurele-Bucharest 76900, Romania
e-mail: dumitru@cankaya.edu.tr
P.O. Box, MG-23, R 76900
,Magurele-Bucharest 76900, Romania
e-mail: dumitru@cankaya.edu.tr
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 2, 2016; final manuscript received November 1, 2017; published online December 7, 2017. Assoc. Editor: Firdaus Udwadia.
J. Comput. Nonlinear Dynam. Feb 2018, 13(2): 021013 (9 pages)
Published Online: December 7, 2017
Article history
Received:
November 2, 2016
Revised:
November 1, 2017
Citation
Hajipour, M., Jajarmi, A., and Baleanu, D. (December 7, 2017). "An Efficient Nonstandard Finite Difference Scheme for a Class of Fractional Chaotic Systems." ASME. J. Comput. Nonlinear Dynam. February 2018; 13(2): 021013. https://doi.org/10.1115/1.4038444
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