Inverse problems for a time fractional diffusion equation in the Schwartz‐type distributions

Abstract

We find the conditions for the unique solvability of the inverse problem of the solution's initial data determination for a time fractional diffusion equation with a Schwartz‐type distribution in the right‐hand side and the inverse problem of identifying the equation's source under given Schwartz‐type distribution in the initial condition. We use a time‐integral overdetermination condition.