Regularity of a fractional partial differential equation driven by space-time white noise

Abstract

Abstract. We will deal with one dimensional stochastic fractional order partial differential equation driven by space-time white noise. The existence and uniqueness of the solution and especially some regularities of the solution are investigated. The regularities of the solution in its time and space variables depend on the relation of the fractional order of its operator and coefficients.

Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

“…Stochastic partial differential equations with fractional Laplacian appear in many fields such as physics, fractal medium, image analysis, risk management and other fields (see Debbi [4], Mueller [12] and Xie [15]). In this paper, we discuss the existence and uniqueness of solutions to the initial value problem for the following stochastic partial differential equation which is denoted by SPDE:…”

A characteristic of fractional resolvents

“…The derivatives and integrals of fractional order are more suitable for describing the properties of various real materials and phenomena, and their theory has gained recently a rapid development (see e.g. Anh and Leonenko [1], Eidelman and Kochubei [3], Hilfer [5], Kilbas et al [7], Niu and Xie [9], Podlubny [11]). …”

Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise

“…It is worth to point out that the authors in [8] study the existence of the mild solution for stochastic fractional Burgers equation driven by Lévy noise, but they could not provide the regularity of the mild solution. The authors in [7,13] study the regularity of the mild solution for stochastic fractional partial differential equations driven by Gaussian white noise, but not Lévy noise. There is a natural question, how about the regularity of the mild solution for the stochastic fraction delayed reaction-diffusion equation driven by Lévy noise?…”