Stochastic pseudo-parabolic equations with fractional derivative and fractional Brownian motion

In this study, fractional stochastic pseudo-parabolic equations driven by fractional Brownian motion are investigated. This work aims at establishing existence, uniqueness, regularity results for mild solutions to an initial value problem for considered equations in two cases of H that are H>12 and H<12. In addition, the continuities of mild solutions with respect to the time variable and the order fractional derivative are constructed.