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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 813535, 12 pages
http://dx.doi.org/10.1155/2012/813535
Research Article

Existence and Uniqueness for Stochastic Age-Dependent Population with Fractional Brownian Motion

School Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China

Received 16 November 2011; Revised 7 January 2012; Accepted 10 January 2012

Academic Editor: Yun-Gang Liu

Copyright © 2012 Zhang Qimin and Li xining. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A model for a class of age-dependent population dynamic system of fractional version with Hurst parameter h(1/2,1] is established. We prove the existence and uniqueness of a mild solution under some regularity and boundedness conditions on the coefficients. The proofs of our results combine techniques of fractional Brownian motion calculus. Ideas of the finite-dimensional approximation by the Galerkin method are used.