Uncertain impulsive differential systems of fractional order: almost periodic solutions

ABSTRACT

In this paper, we investigate the existence and stability of almost periodic solutions of impulsive fractional-order differential systems with uncertain parameters. The impulses are realised at fixed moments of time. For the first time, we determine the impact of the uncertainties on the qualitative behaviour of such systems. The main criteria for the existence of almost periodic solutions are proved by employing the fractional Lyapunov method. The global perfect robust uniform-asymptotic stability of such solutions is also considered. We apply our results to uncertain impulsive neural network systems of fractional order.

KEYWORDS:

• Almost periodic solutions
• impulses
• fractional order
• global perfect robust uniform-asymptotic stability
• Lyapunov method
• uncertain parameters

Acknowledgment

The authors are grateful to the editors and anonymous reviewers for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Gani Stamov

Gani Tr. Stamovreceived his Ph.D. degree from the Higher Accreditation Commission of Bulgaria, and his D.Sci. degree from the University of Chemical Technology and Metallurgy at Sofia, Bulgaria, both in Mathematics, in 1999 and 2011, respectively, He is an author of numerous articles and books in the field of differential equations and applications. His research interests include analysis of dynamical systems, systems of differential equations with fractional derivatives, neural networks, biological systems and models in economics.

Ivanka Stamova

Ivanka M. Stamova received her Ph.D. degree in Differential Equations from the Higher Accreditation Commission of Bulgaria in 1996. In 2009 she received a D.Sci. degree (a degree beyond the Ph.D. degree) in Applied Mathematics from the Higher Accreditation Commission of Bulgaria. She is serving in the Editorial boards of several international high quality mathematical and applied journals. Her current interests include qualitative analysis of dynamical systems, fractional differential equations, impulsive control and applications.