Stochastic fractional heat equation perturbed by general Gaussian and non-Gaussian noise

Abstract

In this work, we study the stochastic heat equation with Caputo derivative perturbed by a class of noises that include Gaussian noises and non-Gaussian noises. We have deduced the existence, uniqueness and pathwise spatial–temporal regularity properties of mild solutions to the corresponding non-linear time-fractional stochastic heat type equation.