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In this article, We investigate an inverse problem of determining thetime-dependent source factor in parabolic integro-differential equations fromboundary data. We establish the uniqueness and the conditional stabilityestimate of H\"older type for the inverse source problem in a cylindricalshaped domain. Our methodology is based on the Bukhgeim-Klibanov method bymeans of the Carleman estimate. Here we also derive the "time-like" Carlemanestimate for parabolic integro-differential equations.

An inverse problem and a time-like Carleman estimate for parabolic integro-differential equations