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