Phuong, Nguyen DucBaleanu, DumitruHoan, Luu Vu CamBaleanu, DumitruNguyen, Anh TuanMatematik2024-01-262024-01-262023Phuong, Nguyen Duc;...et.al. (2023). "Terminal Value Problem For Stochastic Fractional Equation Within An Operator With Exponential Kernel", Fractals, Vol.31, No.4.0218-348X1793-6543https://doi.org/10.1142/S0218348X23400625In 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 W. 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 W? (see Assumption 3.1), which is a subspace of W. When W? is smooth enough, i.e. the parameter ? is sufficiently large, our problem is well-posed and it has a unique solution in the space of Holder continuous functions. In contract, in the different case when ? is smaller, our problem is ill-posed; therefore, we construct a regularization result.eninfo:eu-repo/semantics/openAccessIll-Posed ProblemFractional Stochastic EquationHilbert ScalesCaputo-Fabrizio DerivativeArticle31410.1142/S0218348X234006252-s2.0-85157965630WOS:000978807400002N/AQ1