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Studies on BVPs for IFDEs involved with the Riemann-Liouville type fractional derivatives

100%

Liu Y.

Nonautonomous Dynamical Systems

2016

tom 3

nr 1

42-84

In this article, we present a new method for converting the boundary value problems for impulsive fractional differential systems involved with the Riemann-Liouville type derivatives to integral systems, some existence results for solutions of a class of boundary value problems for nonlinear impulsive fractional differential systems at resonance case and non-resonance case are established respectively. Our analysis relies on the well known Schauder’s fixed point theorem and coincidence degree theory. Examples are given to illustrate main results. This paper is motivated by [Solvability of multi-point boundary value problem of nonlinear impulsive fractional differential equation at resonance, Electron. J. Qual. Theory Differ. Equ. 89(2011), 1-19], [Existence result for boundary value problem of nonlinear impulsive fractional differential equation at resonance, J, Appl, Math, Comput. 39(2012) 421-443] and [Solvability for a coupled system of fractional differential equations with impulses at resonance, Bound. Value Probl. 2013, 2013: 80].

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

100%

Zhang Q., Yang L., Liao D.

International Journal of Applied Mathematics and Computer Science

2011

tom 21

nr 4

649-658

Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

Ograniczanie wyników

1 International Journal of Applied Mathematics and Computer Science

1 Nonautonomous Dynamical Systems

1 Liao D.

1 Liu Y.

1 Yang L.

1 Zhang Q.

1 2016

1 2011

Wyniki wyszukiwania

Studies on BVPs for IFDEs involved with the Riemann-Liouville type fractional derivatives

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays