Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42620161218On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays14791496904ENZ.LiSchool of Information and Mathematics,
Yangtze University, Jingzhou 434023, China.L.XuSchool of Information and Mathematics,
Yangtze University, Jingzhou 434023, China.X.LiSchool of Information and Mathematics,
Yangtze University, Jingzhou 434023, China and
School of Mathematical Sciences,
Beijing Normal University, Beijing 100875, China.Journal Article20150614In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theoryhttp://bims.iranjournals.ir/article_904_070920b9fa736281ee5571ed2c3f208f.pdf