Some aspects of the theory of integro-differential Barbashin equations in function spaces

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We study the solvability conditions for the Cauchy problem for the Barbashin integro-differential equation in the space of bounded continuous functions and in the space of continuous vector-valued functions with the values in an ideal Banach space. We also consider conditions guaranteeing the existence of classical and generalized solutions to the Cauchy problem for systems of linear Barbashin integro-differential equations. Bibliography: 5 titles.