Qualitative Properties of Solutions of Nonlinear Fractional Diffusion Equations Perturbed by a Multiplicative <i>H</i> ‐Regular Space‐Time White Noise

ABSTRACT In this paper, we study analytically an abstract fractional diffusion equation in a Hilbert space with locally Lipschitz sources perturbed by a multiplicative ‐regular space‐time white noise. We first point out the equivalence between classical solutions and mild solutions. Next, we prove the existence, and uniqueness of maximal solutions of the problem and show continuous dependence of solutions on the initial values and associated parameters. Notably, in certain cases, we demonstrate that the solution of the problem is blow‐up in a finite time.