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We study general cordial Volterra integral equations of the second kind and certain singular fractional integro-differential equation in spaces of analytic functions. We characterize properties of the cordial Volterra integral operator in these spaces, including compactness and describe its spectrum. This enables us to obtain conditions under which these equations have a unique analytic solution. We also consider approximate solution of these equations and prove exponential convergence of approximate solutions to the exact solution.

CORDIAL VOLTERRA INTEGRAL EQUATIONS AND SINGULAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN SPACES OF ANALYTIC FUNCTIONS∗