  In this paper, we investigate direct and inverse source problems for the
diffusion equation with two-term generalized fractional derivative (Hilfer
derivative) in a rectangular domain. Using spectral expansion method, we derive
two-term fractional differential equation together with appropriate initial
condition (Cauchy problem). Based on solution of that Cauchy prob\-lem, we
represent solution of formulated problems as a combination of sinus and
multinomial Mittag-Leffler function of two variables. Imposing certain
conditions to the given data, we prove uniform convergence of certain infinite
series.
