Some Numerical Examples on the Stability of Fractional Linear Dynamical Systems
DOI:
https://doi.org/10.12723/mjs.46.5Abstract
The concept of stability of a class of fractional-order linear system is considered in this paper. Existing sufficient conditions are assumed to guarantee the stability of linear models with the Caputo fractional derivatives. The results have been developed by using the concept of Laplace transform, and approximations of Mittag-Leffler. Furthermore, results concerning asymptotical stability of linear fractional-order models are also achieved. The proposed method is based upon Eigen values and the characteristic polynomials. Numerical illustrations are specified to exhibit effectiveness of the proposed method.
References
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[2] A. M. A. El-Sayed, F. M. Gaafar and E. M. A. Hamadalla, “Stability for a nonlocal non-autonomous system of fractional order differential equations with delays,” Electronic Journal of differential Equations, vol. 31, pp. 1-10, 2010.
[3] J.H. He, “Variational iteration method - A kind of non-linear analytical technique: Some examples,” International Journal of Non-Linear Mechanics, vol. 34, pp. 699-708, 1999.
[4] J.H. He, “Homotopy perturbation technique”, Computers and Applied Mechanical Engineering, vol. 178, pp. 257-262, 1999.
[5] Y. Li, Y.Q. Chen, I. Podulbny and Y. Cao, “Mittag-Leffler Stability of Fractional order Non-linear Dynamic Systems,” Automatica, vol. 45, pp. 1965-1969, 2009.
[6] M. P. Lazarevic and A. M. Spasic, “Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach,” Mathematics Computational Modelling, vol. 49, pp. 475-481, 2009.
[7] S. Momani and Z. Odibat, “Numerical approach to differential equation of fractional order,” Applications in Mathematical Computations vol. 201, pp. 96-110, 2007.
[8] I. Podlubny, Fractional Differential Equation. New York: Academic Press, 1999.
[9] S. Priyadharsini, “Stability of Fractional Neutral and integrodifferential Systems,” Journal of Fractional Calculus and Applications, vol. 7, pp. 87-102, 2016.
[10] S. Priyadharsini, “Stability Analysis of Fractional differential Systems with Constant Delay,” Journal of Indian Mathematical Society, vol. 83, pp. 337-350, 2016.
[11] S. Priyadharsini, V. Parthiban and A. Manivannan, “Solution of fractional integrodifferential system with fuzzy initial condition,” International journal of pure and applied mathematics, vol. 8, pp. 107-112, 2016.
[12] M. Zurigat, S. Momani, Z. Odibat and A. Alawneh, “The homotopy analysis method for handling systems of fractional differential equations”, Applications in Mathematical Modelling, vol. 34, pp. 24-35, 2010.
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Published
2018-07-01
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Research Articles
