LYAPUNOV FUNCTION FOR THE STABILITY OF FRACTIONAL DIFFERENTIAL-INTEGRAL RIEMANN-LIOUVILLE
Keywords:
fractional, differential, integral Riemann, Liouville, stabilization, Lyapunov functionsAbstract
In this paper the stability by using the direct method for some Lyapunov functions was applied to the system of fractional-differential-integral Riemann- Liouville type and the results explain the role of the Lyapunov in achieving stability. Some examples have been given to support the results.
References
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2. Y. Li, Yan, Y. Chen, I. Podlubny, Mittag-Leffler stability of fractional order nonlinear dynamic systems, Automatica 45 (2009) 1965–1969.
3. Diethelm, K.: ’The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type’ (Lecture Notes in Mathematics 2004, Springer-Verlag, Berlin, 2010).
4. Vainikko, G.: ’Which functions are fractionally differentiable?’, Journal of Analysis and its Applications, 2016, 35, pp. 465–487.
5. Rockafellar, R.T.: ’Convex Analysis’ (Princeton University Press, Princeton, New Jersey, 1972).
6. Li, Y., Chen, Y., Podlubny, I.: ’Mittag-Leffler stability of fractional order nonlinear dynamic systems’, Automatica, 2009, 45, pp. 1965–1969.
7. Aguila-Camacho, N., Duarte-Mermoud, M.A., Gallegos, J.A.: ’Lyapunov functions for fractional order systems’, Commun Nonlinear Sci Numer Simulat., 2014, 19, (9), pp. 2951–2957.
8. Chen, W., Dai, H., Song, Y., Zhang, Z.: ’Convex Lyapunov functions for stability analysis of fractional order systems’, IET Control Theory Appl., 2017, 11, (5), pp. 1070–1074.
9. Baleanu, D., Mustafa, O.: ’On the global existence of solutions to a class of fractional differential equations’, Computers and Mathematics with Applications, 2010, 59, pp. 1835–1841.
10. Heinonen, J.: ’Lectures on Lipschitz Analysis’ (Technical Report, University of Jyväskylä, 2005).
11. Chen, W., Dai, H., Song, Y., Zhang, Z.: ’Convex Lyapunov functions for stability analysis of fractional order systems’, IET Control Theory Appl., 2017, 11, (5), pp. 1070–1074.
12. Feng, Y., Li, L., Liu, J., Xu, X.: ’Continuous and discrete one dimensional autonomous fractional odes’, Discrete and Continuous Dynamical Systems-Series B, doi:10.3934/dcdsb.2017210.
13. Aghababa, M.P.: ’Stabilization of a class of fractional-order chaotic systems using a non-smooth control methodology’, Nonlinear Dyn., 2017, 89, (2), pp. 1357–1370.
14. Zhou, X.F., Hu, L.G., Jiang, W.: ’Stability criterion for a class of nonlinear fractional differential systems’, Applied Mathematics Letters, 2014, 28, pp. 25–29.
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Published
2024-01-08
How to Cite
Mohammed Ghazi, Dr. Faruk POLAT, & Dr. Sameer Qasim HASAN. (2024). LYAPUNOV FUNCTION FOR THE STABILITY OF FRACTIONAL DIFFERENTIAL-INTEGRAL RIEMANN-LIOUVILLE. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 5(1), 6–23. Retrieved from https://cajmtcs.casjournal.org/index.php/CAJMTCS/article/view/594
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