Reconstruction of time-dependent source term in fractional diffusion equations with Hilfer derivative

We propose to study an inverse source problem for one dimensional generalized fractional diffusion model with Hilfer derivative. Our objective is to obtain formulas and algorithms for reconstructing the time-dependent source term for a class of initial boundary value problems with nonlocal boundary conditions supplemented with additional measurement data. In addition, we aim to determine some sufficient regularity conditions for the well-posedness of the solution. To achieve our objectives we shall use the Fourier series method, transform and operational methods for fractional differential equations, generalized Mittag-Leffler function properties, and uniform convergence tests. We shall also verify the analytical results by numerical experiments. We expect the results of this study to be of interest in a wide range of applications where anomalous diffusion takes place.