Stochastic sub-diffusion equation with conformable derivative driven by standard Brownian motion

Year 2021, , 287 - 299, 30.09.2021

Ngo Hung Ho Binh Nguyen Luc , An Nguyen Thı Kıeu Le Dinh Long

https://doi.org/10.31197/atnaa.906952

Cited By: 3

Abstract

This article is concerned with a forward problem for the following sub-diffusion equation driven by standard Brownian motion
\begin{align*}
\left( ^{\mathcal C} \partial^\gamma_t + A \right) u(t) = f(t) + B(t) \dot{W}(t), \quad t\in J:=(0,T),
\end{align*}
where $^{\mathcal C} \partial^\gamma_t$ is the conformable derivative, $\gamma \in (\frac{1}{2},1].$ Under some flexible assumptions on $f,B$ and the initial data, we investigate the existence, regularity, continuity of the solution on two spaces $L^r(J;L^2(\Omega,\dot{H}^\sigma))$ and $C^\alpha(\overline{J};L^2(\Omega,H))$ separately.

Keywords

Diffusion equation, Standard Brownian motion, Fractional Brownian motion, Existence and regularity., Conformable derivative

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