  In the present work, we discuss a unique solvability of an inverse-source
problem with integral transmitting condition for time-fractional mixed type
equation in a rectangular domain, where the unknown source term depends on
space variable only.
  The method of solution based on a series expansion using bi-orthogonal basis
of space corresponding to a nonself-adjoint boundary value problem. Under
certain regularity conditions on the given data, we prove the uniqueness and
existence of the solution for the given problem. Influence of transmitting
condition on the solvability of the problem is shown as well. Precisely, two
different cases were considered; a case of full integral form ($0<\gamma<1$)
and a special case ($\gamma=1$) of transmitting condition.
  In order to simplify the bulky expressions appearing in the proof of the main
result, we have established a new property of the recently introduced
Mittag-Leffler type function of two variables (see Lemma 2.1).
