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We consider mixed problems for infinite systems of first order partial functional differential equations. Infinite number of deviating functions is permitted, and the delay of an argument may depend also on spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral systems can be derived from the general model by specializing given operators. AMS Subject Classifications: 35R10, 35F25.

Infinite systems of first order PFDEs with mixed conditions