Robust Stability of Implicit Dynamic Equations with Nabla Derivative on Time Scales
Main Article Content
Abstract
In this work we studied the robust stability for implicit integro-dynamic equations on time scales with nabla derivative, which is considered as a generation of differential algebraic equations and implicit difference equations. We showed the reservation of exponential stability of these equations under small Lipschitz perturbations.
Keywords:
Implicit integro-dynamic equations, index 1, uniformly stability, time scale, Lipschitz perturbations.
References
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[2] H. Brunner, Volterra Integral Equations: an Introduction to Theory and Applications, University Printing House, Cambridge CB2 8BS, United Kingdom, 2017.
[3] L. D. Yu, M. G. Krein, M. G, Stability of Solutions of Differential Equations in Banach Space, Amer. Math. Soc., Providence, RI, 1971.
[4] N. H. Du, N. H. Linh, V. H. Nga, N. T. T. On, Stability and Bohl Exponent of Linear Singular Systems of Difference Equations with Variable Coefficients, J. Differ. Equ. Appl., Vol 22, 2016, pp. 1350-1377, https://doi.org/10.1080/10236198.2016.1198341.
[5] R. Agarwal, Donal O'Regan, Samir Saker-Dynamic Inequalities On Time Scales-Springer, 2014.
[6] S. K. Choi, N. Koo, On a Gronwall-type inequality on time scales. Journal of the Chungcheong Maththematica Society, Vol. 23, No. 1, 2010, pp 137-147, https://doi.org/10.14403/jcms.2010.23.1.137 .
[7] G. S. Guseinov, Integration on Time Scales, J. Math. Anal. Appl., Vol. 285, No.1, 2003, pp. 107-127, https://doi.org/10.1016/S0022-247X(03)00361-5.
[8] R. Marz, Extra-ordinary Differential Equation: Attempts to An Analysis of Differential Algebraic System, Progress in Mathematics, Vol. 168, 1998, pp. 313-334, https://doi.org/10.18452/2708.