On fractional diffusion equation with noise perturbation

The stochastic time-fractional diffusion equation can be accounted for a logical description of models with subdiffusion. This work is dedicated to the study of existence and uniqueness of the solution of stochastic time-fractional diffusion equation perturbed with a nonlinear source term. The method of Faedo–Galerkin approximations is employed in order to arrive at the estimate and to establish existence of solution by assuming that the noise coefficient and the nonlinear source term satisfy the required assumptions like Lipschitz continuity and linear growth condition.