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In the present work, we discuss a unique solvability of an inverse-sourceproblem with integral transmitting condition for time-fractional mixed typeequation in a rectangular domain, where the unknown source term depends onspace variable only.  The method of solution based on a series expansion using bi-orthogonal basisof space corresponding to a nonself-adjoint boundary value problem. Undercertain regularity conditions on the given data, we prove the uniqueness andexistence of the solution for the given problem. Influence of transmittingcondition on the solvability of the problem is shown as well. Precisely, twodifferent 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 mainresult, we have established a new property of the recently introducedMittag-Leffler type function of two variables (see Lemma 2.1).

Inverse source non-local problem for mixed type equation with Caputo fractional differential operator