Identifying an unknown coefficient in the fractional parabolic differential equation

In this study, we considered a fractional parabolic equation for identifying the unknown diffusion coefficient from noisy measurement of ultimate time solution. It is an inverse problem involving nonlocal operator that nonlinear and poorly formulated. By demonstrating existence singular solution with regard to final observed data, demonstrate identifiability problem. The expressed as regularized optimization minimizes cost function least-squares kind. We have covered various theoretical practical difficulties pertaining under consideration. has been demonstrated unique stable exists. Morozov discrepancy principle conjugate gradient approach are used develop iterative reconstruction procedure. accuracy efficiency suggested method illustrated using few numerical examples.