Abstract
This article is devoted to the study of the attractivity of solutions to a class of stochastic evolution equations involving Hilfer fractional derivative. By employing the semigroup theory, fractional calculus and the fixed point technique, we establish new alternative criteria to ensure the existence of globally attractive solutions for the Cauchy problem when the associated semigroup is compact.
Highlights
In the past three decades, fractional differential equations received much attention
Chen et al [6] established the global attractivity for nonlinear fractional differential equations
It is important and necessary to consider stochastic perturbation into the investigation of fractional differential equations. It seems that there is less literature related to the stability of Hilfer fractional stochastic evolution equations
Summary
In the past three decades, fractional differential equations received much attention. Et al [11] studied the attractivity of solutions for a class of multi-term fractional functional differential equations. The attractivity of solutions of Hilfer fractional stochastic evolution equations might be a fascinating and useful problem. We study the attractivity of solutions for the following Hilfer fractional stochastic evolution equations:. Theorem 2.1 ([5]) Let S be a nonempty, closed, convex and bounded subset of the Banach space X and let A : X → X and B : S → X be two operators such that (a) A is a contraction with constant L < 1, (b) B is continuous, BS resides in a compact subset of X, (c) [x = Ax + By, y ∈ S] ⇒ x ∈ S.
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