Affiliation:
1. School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, China
Abstract
<p style='text-indent:20px;'>This paper is concerned with stochastic delay evolution equations driven by tempered fractional Brownian motion (tfBm) <inline-formula><tex-math id="M1">\begin{document}$ B_Q^{\sigma, \lambda}(t) $\end{document}</tex-math></inline-formula> with time fractional operator of order <inline-formula><tex-math id="M2">\begin{document}$ \alpha\in (1/2+\sigma, 1) $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M3">\begin{document}$ \sigma\in (-1/2, 0) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \lambda>0 $\end{document}</tex-math></inline-formula>. First, we establish the global existence and uniqueness of mild solutions by using the new established estimation of stochastic integrals with respect to tfBm. Moreover, based on the relations between the stochastic integrals with respect to tfBm and fBm, we show the continuity of mild solutions for stochastic delay evolution equations when tempered fractional noise is reduced to fractional noise. Finally, we analyze the stability with general decay rate (including exponential, polynomial and logarithmic stability) of mild solutions for stochastic delay evolution equations with tfBm and time tempered fractional operator.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis