Weak Solution for a Time-fractional Parabolic Problem with Application to an Inverse Problem

Abstract

In this paper, we consider a parabolic equation involving Caputo’s time-fractional derivative of order α ∈ (0, 1), called subdiffusion problem. We obtain existence, uniqueness and stability results of weak solution for the reaction-diffusion problem in view of fixed point theory. Then, we study an inverse coefficient problem with an output data g(t) for a fixed point space.