Inverse problem for a time-fractional differential equation with a time- and space-integral conditions

We study the inverse problem for a differential equation of order 2b$$ 2b $$ with the time Caputo fractional derivative and a source with values in Schwartz-type distributions. The generalized solution of the Cauchy problem for such an equation with initial values and a time-dependent reaction coefficient are unknown. We find sufficient conditions for the unique solvability of the inverse problem under a time- and space-integral overdetermination conditions.