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

Abstract

We study the inverse problem for a differential equation of order 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.