Stability analysis of nonlinear Riemann-Liouville fractional differential equations
DOI :
https://doi.org/10.5269/bspm.62981Résumé
In this paper, we give sufficient conditions to guarantee the asymptotic stability of the zero solution to a kind of nonlinear fractional differential equations with the Riemann Liouville fractional derivative of order α∈(n-1,n) by using Krasnoselskii's fixed point theorem and the Banach contraction mapping principle in a weighted Banach space. The results obtained here extend the work of Li and Kou [6].
Références
1. Agarwal, R. P., Zhou, Y., He, Y., Existence of fractional functional differential equations, Comput. Math. Appl. 59, 1095-1100, (2010).
2. Ge, F., Kou, C., Asymptotic stability of solutions of nonlinear fractional differential equations of order 1 < α < 2, J. Shanghai Normal Univ. 44(3), 284-290, (2015).
3. Kilbas, A. A., Srivastava, H. M., Trujillo, J. J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, (2006).
4. Kou, C., Zhou, H., Yan, Y., Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis, Nonlinear Anal. 74, 5975-5986, (2011).
5. Li, Y., Chen, Y., Podlunby, I., Mittag-Leffler stability of fractional order nonlinear dynamic systems, Automatica 45, 1965-1969, (2009).
6. Li, J., Kou, C., Stability analysis of nonlinear fractional differential equations by fixed point theorem, Commun. Appl. Math. Comput. 32(3), 772-785, (2018).
7. Li, C., Zhang, F., A survey on the stability of fractional differential equations, Eur. Phys. J. Special Topics 193, 27-47, (2011).
8. Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, (1999).
9. Smart, D. R., Fixed Point Theorems, Cambridge University Press, Cambridge, (1980).
10. Wang, J., Zhou, Y., Feckan, M., Nonlinear impulsive problems for fractional differential equations and Ulam stability, Comput. Math. Appl. 64, 3389-3405, (2012).
11. Wang, Z. L., Yang, D. S., Ma, T. D., Sun, N., Stability analysis for nonlinear fractional-order systems based on comparison principle, Nonlinear Dyn. 75, 387-402, (2014).
2. Ge, F., Kou, C., Asymptotic stability of solutions of nonlinear fractional differential equations of order 1 < α < 2, J. Shanghai Normal Univ. 44(3), 284-290, (2015).
3. Kilbas, A. A., Srivastava, H. M., Trujillo, J. J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, (2006).
4. Kou, C., Zhou, H., Yan, Y., Existence of solutions of initial value problems for nonlinear fractional differential equations on the half-axis, Nonlinear Anal. 74, 5975-5986, (2011).
5. Li, Y., Chen, Y., Podlunby, I., Mittag-Leffler stability of fractional order nonlinear dynamic systems, Automatica 45, 1965-1969, (2009).
6. Li, J., Kou, C., Stability analysis of nonlinear fractional differential equations by fixed point theorem, Commun. Appl. Math. Comput. 32(3), 772-785, (2018).
7. Li, C., Zhang, F., A survey on the stability of fractional differential equations, Eur. Phys. J. Special Topics 193, 27-47, (2011).
8. Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, (1999).
9. Smart, D. R., Fixed Point Theorems, Cambridge University Press, Cambridge, (1980).
10. Wang, J., Zhou, Y., Feckan, M., Nonlinear impulsive problems for fractional differential equations and Ulam stability, Comput. Math. Appl. 64, 3389-3405, (2012).
11. Wang, Z. L., Yang, D. S., Ma, T. D., Sun, N., Stability analysis for nonlinear fractional-order systems based on comparison principle, Nonlinear Dyn. 75, 387-402, (2014).
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Publié
2025-01-21
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Research Articles
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