Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 46, Issue 7, Pages 7725-7740Publisher
WILEY
DOI: 10.1002/mma.7125
Keywords
fractional Brownian motion; fractional differential equation; fractional noise; Rayleigh– Stokes equation; stochastic partial differential equation
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In this work, a stochastic Rayleigh-Stokes equation driven by fractional Brownian motion is investigated in different parameter ranges, and the existence, uniqueness, and regularity results of the mild solutions are established.
In this work, a stochastic Rayleigh-Stokes equation driven by fractional Brownianmotion is considered in both cases h epsilon. ( 0, 1/2) and h epsilon ( 1/22, 1). The existence and uniqueness of mild solution in each case are established separately by applying a standard method that is Banach fixed point theorem. The required results are obtained by stochastic analysis techniques, fractional calculus. In addition, the regularity results of mild solution for this problem is investigated.
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