Intermittence and space-time fractional stochastic partial differential equations (Q259212)

This paper carries on the study of a time-fractional stochastic heat type equation involving a Caputo fractional derivative, a fractional Laplacian and the fractional integral of a space-time white noise. This equation may be used to model phenomena in a material with thermal memory and random effects. The authors have proved the existence and uniqueness of solutions for this equation in a previous paper [Stochastic Process. Appl. 125, No. 9, 3301--3326 (2015; Zbl 1329.60216)]. In the present study, they prove weak intermittency of the solution as already known for parabolic-type SPDEs. When restricting to the real time-fractional stochastic heat equation, they also prove that the distances to the origin of the farthest high peaks of the moments grow exactly linearly with time.