In this paper, we prove the unique solvability of an analogue problem Darboux for a loaded integro-differential equation with Caputo operator by method of integral equations. The problem is equivalently reduced to a system of integral equations, which is unconditionally and uniquely solvable.

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No abstract

In the work was found an explicit formula of a solution of analog of a Cauchy problem for a loaded multidimensional partial differential equation of a higher order.