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Nonlinear delay integrodifferential systems with Caputo fractional derivative in infinite-dimensional spaces

100%
Wang J., Wei W.
Annales Polonici Mathematici
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2012
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tom 105
|
nr 3
209-223
EN
This paper is mainly concerned with existence of mild solutions and optimal controls for nonlinear delay integrodifferential systems with Caputo fractional derivative in infinite-dimensional spaces. We do not assume that the relevant strongly continuous semigroup is compact.
2
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Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses

81%
Fečkan M., Wang J., Zhou Y.
Nonautonomous Dynamical Systems
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2014
|
tom 1
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nr 1
EN
In this paper, we consider periodic solutions for a class of nonlinear evolution equations with non-instantaneous impulses on Banach spaces. By constructing a Poincaré operator, which is a composition of the maps and using the techniques of a priori estimate, we avoid assuming that periodic solution is bounded like in [1-4] and try to present new sufficient conditions on the existence of periodic mild solutions for such problems by utilizing semigroup theory and Leray-Schauder's fixed point theorem. Furthermore, existence of a global compact connected attractor for the Poincaré operator is derived.
3
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On the nonlocal Cauchy problem for semilinear fractional order evolution equations

81%
Wang J., Zhou Y., Fečkan M.
Open Mathematics
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2014
|
tom 12
|
nr 6
911-922
EN
In this paper, we develop the approach and techniques of [Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam. Systems Appl., 2007, 16(3), 507–516], [Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations, Nonlinar Anal. Real World Appl., 2010, 11(5), 4465–4475] to deal with nonlocal Cauchy problem for semilinear fractional order evolution equations. We present two new sufficient conditions on existence of mild solutions. The first result relies on a growth condition on the whole time interval via Schaefer fixed point theorem. The second result relies on a growth condition splitted into two parts, one for the subinterval containing the points associated with the nonlocal conditions, and the other for the rest of the interval via O’Regan fixed point theorem.
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