Research Papers

The Fractional Linear Systems of Equations Within an Operational Approach

[+] Author and Article Information
Dumitru Baleanu

Department of Mathematics and Computer Science,
Çankaya University,
06530 Balgat, Ankara, Turkey;
Institute of Space Sciences, Magurele-Bucharest,
R 76911, Romania
e-mail: dumitru@cankaya.edu.tr

Abbas Saadatmandi

Faculty of Mathematical Sciences,
Department of Applied Mathematics,
University of Kashan,
Kashan 87317-51167, Iran
e-mail: saadatmandi@kashanu.ac.ir

Abdelouahab Kadem

Faculty of Sciences,
Mathematics Department,
University of Setif,
Setif, Algeria,
e-mail: abdeluoahabk@yahoo.fr

Mehdi Dehghan

Faculty of Mathematics and Computer Science,
Department of Applied Mathematics,
Amirkabir University of Technology,
No. 424, Hafez Ave., Tehran, Iran
e-mail: mdehghan@aut.ac.ir

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received May 3, 2012; final manuscript received July 2, 2012; published online August 31, 2012. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 8(2), 021011 (Aug 31, 2012) (6 pages) Paper No: CND-12-1068; doi: 10.1115/1.4007192 History: Received May 03, 2012; Revised July 02, 2012

Fractional calculus is a rapidly going area from both experimental and theoretical points of view. As a result new methods and techniques should be developed in order to deal with new types of fractional differential equations. In this paper the operational matrix of fractional derivative together with the τ method are used to solve the linear systems of fractional differential equations. The results of this method are shown by solving three illustrative examples. By comparing the obtained results with the analytic solutions and with the ones provided by three standard methods for solving the fractional differential equations we conclude that our method gave comparable results.

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Grahic Jump Location
Fig. 1

Plot of y1(x) (line) and y2(x) (point) for m = 7 and with α1 = 0.7,α2 = 0.9 from example 2

Grahic Jump Location
Fig. 2

Plot of error functions |y1*(x)-y1(x)| (left) and |y2*(x)-y2(x)| (right) for m = 7 and α1 = α2 = 1 from example 2

Grahic Jump Location
Fig. 3

Exact (right) and approximate solutions (left) with m = 5 and α = 0.95 from example 3

Grahic Jump Location
Fig. 4

Exact (right) and approximate solutions (left) with m = 5 and α = 0.85 from example 3

Grahic Jump Location
Fig. 5

Plot of error functions |y1*(x)-y1(x)| (left) and |y2*(x)-y2(x)| (right) for m = 13 and α = 0.98 from example 3




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