Stochastic solutions for time-fractional heat equations with complex spatial variables

Abstract We deal with complex spatial diffusion equations time-fractional derivative and study their stochastic solutions. In particular, we complexify the integral operator solution to heat-type equation where time is replaced convolution-type generalization of regularized Caputo derivative. prove that this a heat variable. This approach leads wrapped Brownian motion on circle time-changed by inverse related subordinator. analyzed and, in some results its moments, as well construction weak limit continuous-time random walks, are obtained. The extension our higher dimensional case also provided.