  In the present work, we investigate a uniqueness of solution of the inverse
source problem with non-local conditions for mixed parabolic-hyperbolic type
equation with Caputo fractional derivative. Solution of the problem we
represent as bi-orthogonal series with respect to space variable and will get
fractional order differential equations with respect to time-variable. Using
boundary and gluing conditions, we deduce system of algebraic equations
regarding unknown constants and imposing condition to the determinant of this
system, we prove a uniqueness of considered problem. Moreover, we find some
non-trivial solutions of the problem in case, when imposed conditions are not
fulfilled.
