Stochastic solutions of generalized time-fractional evolution equations

Abstract We consider a general class of integro-differential evolution equations which includes the governing equation generalized grey Brownian motion and time- space-fractional heat equation. present relation between parameters distribution underlying stochastic processes, as well discuss different classes processes providing solutions these equations. For subclass equations, containing Marichev-Saigo-Maeda time-fractional operators, we determine corresponding explicitly. Moreover, explain how self-similar with stationary increments can be obtained via linear fractional Lévy for suitable pseudo-differential operators in space.