Rocky Mountain Journal of Mathematics

Practical stability analysis with respect to manifolds and boundedness of differential equations with fractional-like derivatives

Anatoliy Martynyuk, Gani Stamov, and Ivanka Stamova

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Abstract

In this paper, a new approach for studying the practical stability and boundedness with respect to a manifold of the solutions of a class of fractional differential equations is applied. The technique is based on the recently defined ``fractional-like derivative'' of Lyapunov-type functions. Sufficient conditions using vector Lyapunov functions are established. Examples are also presented to illustrate the theory.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 1 (2019), 211-233.

Dates
First available in Project Euclid: 10 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1552186959

Digital Object Identifier
doi:10.1216/RMJ-2019-49-1-211

Mathematical Reviews number (MathSciNet)
MR3921874

Zentralblatt MATH identifier
07054933

Subjects
Primary: 34A08: Fractional differential equations
Secondary: 34D20: Stability 34D35: Stability of manifolds of solutions

Keywords
Fractional-like derivative Lyapunov method practical stability boundedness manifolds

Citation

Martynyuk, Anatoliy; Stamov, Gani; Stamova, Ivanka. Practical stability analysis with respect to manifolds and boundedness of differential equations with fractional-like derivatives. Rocky Mountain J. Math. 49 (2019), no. 1, 211--233. doi:10.1216/RMJ-2019-49-1-211. https://projecteuclid.org/euclid.rmjm/1552186959


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