Identification of the Time‐Dependent Coefficients in the Fractional Diffusion Equation With Two‐Point Boundary Conditions

ABSTRACT In this article, we investigate an inverse problem of identifying a time‐dependent coefficient in a time‐fractional diffusion equation with two‐point boundary conditions. The unknown coefficient is recovered from an overdetermination condition prescribed at the midpoint of the spatial interval. Since the corresponding boundary conditions are not strongly regular, the direct Fourier method cannot be applied to the original spectral problem. We overcome this difficulty by decomposing the solution into symmetric and antisymmetric parts and reducing the original problem to two auxiliary problems.