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The Cauchy type problem for a differential equation with fractional derivative and self-adjoint operator in a Hilbert space is considered. The problem of parameter determination in equation by the value of the solution at a fixed point is presented. Theorems of existence and uniqueness of the solution are proved.doi:10.17516/1997-1397-2015-8-1-55-63 fatcat:wki5rl74qfha3ns23ww5habtte