Affiliation:
1. Department of Mathematics, Northwest Normal University Lanzhou 730070, People’s Republic of China
Abstract
Abstract
In this article, we are concerned with a class of fractional stochastic evolution equations with nonlocal initial conditions in Hilbert spaces. The existence of mild solutions is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions by using fractional calculations, Schauder fixed point theorem, stochastic analysis theory, α-order fractional solution operator theory and α-resolvent family theory. The results obtained in this paper improve and extend some related conclusions on this topic. An example is also given to illustrate the feasibility of our abstract result.
Subject
Applied Mathematics,Analysis
Reference50 articles.
1. D. Araya, C. Lizama, Almost automorphic mild solutions to fractional differential equations. Nonlinear Anal.69, No 11 (2008), 3692–3705.
2. E.G. Bajlekova, Fractional Evolution Equations in Banach Spaces. PhD Thesis, Department of Mathematics, Eindhoven University of Technology (2001).
3. J. Bao, Z. Hou, Existence of mild solutions to stochastic neutral partial functional differential equations with non-Lipschitz coefficients. Comput. Math. Appl.59, No 1 (2010), 207–214.
4. J. Bao, Z. Hou, C. Yuan, Stability in distribution of mild solutions to stochastic partial differential equations. Proc. Amer. Math. Soc.138, No 6 (2010), 2169–2180.
5. A. Boucherif, Semilinear evolution inclutions with nonlocal conditions. Appl. Math. Letters22, No 8 (2009), 1145–1149.