Some Properties of Fractional Kinetic Equation with Gaussian Noise Rough in Space

In this article, we study a class of fractional kinetic equation driven by Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst index H<1/2 in space. By using the techniques of Malliavin calculus, we prove the existence of the solution in the Skorohod sense and establish the upper and lower bounds for the moments of the solution. We also deduce the H\"older continuity of the solution with respect to the time and space variables.