Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise.
- Resource Type
- Article
- Authors
- Li, Ziqiang; Yan, Yubin
- Source
- Fractional Calculus & Applied Analysis. Apr2024, Vol. 27 Issue 2, p487-518. 32p.
- Subject
- *BANACH spaces
*NOISE
*RIESZ spaces
- Language
- ISSN
- 1311-0454
We investigate a semilinear stochastic time-space fractional subdiffusion equation driven by fractionally integrated multiplicative noise. The equation involves the ψ -Caputo derivative of order α ∈ (0 , 1) and the spectral fractional Laplacian of order β ∈ (1 2 , 1 ] . The existence and uniqueness of the mild solution are proved in a suitable Banach space by using the Banach contraction mapping principle. The spatial and temporal regularities of the mild solution are established in terms of the smoothing properties of the solution operators. [ABSTRACT FROM AUTHOR]