Stochastic fractional diffusion equations containing finite and infinite delays with multiplicative noise

Article type: Research Article

Authors: Tuan, Nguyen Huy^{a; b} | Caraballo, Tomás^c | Thach, Tran Ngoc^{d; *}

Affiliations: [a] Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam | [b] Faculty of Applied Technology, School of Engineering and Technology, Van Lang University, Ho Chi Minh City, Vietnam | [c] Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, C/ Tarfia s/n, 41012 – Sevilla, Spain | [d] Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

Correspondence: [*] Corresponding author. E-mail: tranngocthach@tdtu.edu.vn.

Abstract: In this work, we investigate stochastic fractional diffusion equations with Caputo–Fabrizio fractional derivatives and multiplicative noise, involving finite and infinite delays. Initially, the existence and uniqueness of mild solution in the spaces Cp([−a,b];Lq(Ω,H˙r))) and Cδ((−∞,b];Lq(Ω,H˙r))) are established. Next, besides investigating the regularity properties, we show the continuity of mild solutions with respect to the initial functions and the order of the fractional derivative for both cases of delay separately.

Keywords: Fractional diffusion equations, standard Brownian motion, finite delay, infinite delay, stochastic equations

DOI: 10.3233/ASY-221811

Journal: Asymptotic Analysis, vol. 133, no. 1-2, pp. 227-254, 2023