Stochastic sub-diffusion equation with conformable derivative driven by standard Brownian motion
Keywords:
Diffusion equation, Standard Brownian motion, Fractional Brownian motion, Existence and regularity., Conformable derivativeAbstract
This article is concerned with a forward problem for the following sub-diffusion equation driven by standard Brownian motion
(C∂γt+A)u(t)=f(t)+B(t)˙W(t),t∈J:=(0,T),(�∂��+�)�(�)=�(�)+�(�)�˙(�),�∈�:=(0,�),
where C∂γt�∂�� is the conformable derivative, γ∈(12,1].�∈(12,1]. Under some flexible assumptions on f,B�,� and the initial data, we investigate the existence, regularity, continuity of the solution on two spaces Lr(J;L2(Ω,˙Hσ))��(�;�2(Ω,�˙�)) and Cα(¯¯¯¯J;L2(Ω,H))��(�¯;�2(Ω,�)) separately.
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