m-Dissipativity for Kolmogorov Operator of a Fractional Burgers Equation with Space-time White Noise

Stochastic Burgers’ equation with fractional derivative driven by multiplicative noise

“…The main contribution of this paper is to establish the existence, uniqueness, and regularity properties of mild solution to time-space fractional SBE driven by multiplicative noise, which generalizes many previous works [6,11,12]. The rest of the paper is organized as follows.…”

“…Brzeźniak et al [6] studied the ergodic properties of the solution for space-fractional SBE. Yang [11] proposed some estimates on the solution of space-fractional SBE and given the invariant measure. Lv and Duan [12] investigated the existence of martingale solutions and weak solutions for space-fractional SBE on a bounded domain.…”

Numerical analysis of finite element method for time‐fractional Cahn‐Hilliard‐Cook equation

“…Now we will prove the regularity results of mild solution to semidiscrete scheme (15). To do this, we consider a subset…”

“…Theorem 3.1. For any 0 ≤ ≤ 1 and 0 ≤ ≤ ≤ 2, let u h (t) be the unique mild solution to (15), then there exists a constant C such that sup…”

“…Moreover, fractional differential equations provide a natural description of long memory processes, which have been increasingly interesting owning to their applications in many fields, such as physics, fluid flow, and engineering. [11][12][13][14] Currently, one can also find a large body of significant development in theoretical analysis and numerical methods of fractional calculus; see the previous studies [15][16][17][18][19][20][21][22] and the references therein.…”