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

Authors : Ngo HUNG, Ho BİNH, Nguyen LUC, An NGUYEN THI KIEU, Le Dinh LONG

Pages : 287-299

Doi:10.31197/atnaa.906952

View : 11 | Download : 15

Publication Date : 2021-09-30

Article Type : Research Paper

Abstract :This article is concerned with a forward problem for the following sub-diffusion equation driven by standard Brownian motion \begin{align*} \leftinsert ignore into journalissuearticles values( ^{\mathcal C} \partial^\gamma_t + A \right); uinsert ignore into journalissuearticles values(t); = finsert ignore into journalissuearticles values(t); + Binsert ignore into journalissuearticles values(t); \dot{W}insert ignore into journalissuearticles values(t);, \quad t\in J:=insert ignore into journalissuearticles values(0,T);, \end{align*} where $^{\mathcal C} \partial^\gamma_t$ is the conformable derivative, $\gamma \in insert ignore into journalissuearticles values(\frac{1}{2},1].$ Under some flexible assumptions on $f,B$ and the initial data, we investigate the existence, regularity, continuity of the solution on two spaces $L^rinsert ignore into journalissuearticles values(J;L^2insert ignore into journalissuearticles values(\Omega,\dot{H}^\sigma););$ and $C^\alphainsert ignore into journalissuearticles values(\overline{J};L^2insert ignore into journalissuearticles values(\Omega,H););$ separately.
Keywords : Diffusion equation, Standard Brownian motion, Fractional Brownian motion, Existence and regularity, Conformable derivative