Abstract. For a time fractional diffusion equation and diffusion-wave equation with Caputo partial derivatives we prove the correctness of an inverse problem. This problem is to find a solution of direct problem, which is classical in time with values in the space of periodic spatial distributions, and a source term of the equation. A time integral over-determination condition is used.Mathematics subject classification (2010): 35S10.

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iqutions with frtionl derivtives nd inverse prolems for them rise in mny rnhes of siene nd engineering with memory eing tken into ountF ome inverse prolems to di'usionEwve equtions with di'erent unknown funtions or prmeters @soureD order of prtil derivtiveD older or minor oe0ientD oundry or initil dtA were investigtedD for exmpleD in IEIIF sn prtiulrD in ID QD RD TD U integrl type overEdetermintion onditions were used in the inverse soure nd oe0ient prolems for suh equtionsF sn this pperD we (nd the onditions of uniqueness of the solution (u, g) of the inverse prolem D α t u − ∆u = g(t)F

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