Publication:
TERMINAL VALUE PROBLEM FOR STOCHASTIC FRACTIONAL EQUATION WITHIN AN OPERATOR WITH EXPONENTIAL KERNEL
TERMINAL VALUE PROBLEM FOR STOCHASTIC FRACTIONAL EQUATION WITHIN AN OPERATOR WITH EXPONENTIAL KERNEL
No Thumbnail Available
Files
Date
2023
Authors
NGUYEN DUC PHUONG
LUU VU CAM HOAN
DUMITRU BALEANU
ANH TUAN NGUYEN
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
Organizational Units
Journal Issue
Abstract
<jats:p>In this paper, we investigate a terminal value problem for stochastic fractional diffusion equations with Caputo–Fabrizio derivative. The stochastic noise we consider here is the white noise taken value in the Hilbert space [Formula: see text]. The main contribution is to investigate the well-posedness and ill-posedness of such problem in two distinct cases of the smoothness of the Hilbert scale space [Formula: see text] (see Assumption 3.1), which is a subspace of [Formula: see text]. When [Formula: see text] is smooth enough, i.e. the parameter [Formula: see text] is sufficiently large, our problem is well-posed and it has a unique solution in the space of Hölder continuous functions. In contract, in the different case when [Formula: see text] is smaller, our problem is ill-posed; therefore, we construct a regularization result.</jats:p>
Description
Keywords
"Ill-Posed Problem,
Fractional Stochastic Equation,
Hilbert Scales,
Caputo–Fabrizio Derivative."