Inverse Cauchy problem for fractional diffusion equation with generalized functions in the right-hand sides

Abstract

We establish the unique solvability of the inverse Cauchy problem for a time fractional diffusion equation with distributions in the right-hand sides of the equation and in the initial condition. This problem is to find the pair of the following functions: the generalized solution (continuous in time in generalized sense) of direct Cauchy problem and the unknown minor coefficient (depending on the time variable) of the equation.