Problem without initial conditions for equation with fractional derivatives and intermediate asymptotics

The correct solvability of problems without initial conditions for fractional-power operator sums is shown. Solutions of problems without initial conditions are interpreted by Ya.B. Zeldovich and G.I. Barenblatt as intermediate asymptotics for problems with initial conditions. These authors point out the importance of such problems in connection with the expansion of the concept of "strict determinism" in statistical physics and quantum mechanics and raise the question of studying the properties of phenomena that do not depend on details in the initial conditions that manifest themselves after sufficient time. The present paper also provides an example of intermediate asymptotics for an equation with a fractional derivative.