https://doi.org/10.71352/ac.54.341
On solvability of Barbashin's type equation and
initial value problem via the structure of
generalized convolutions
Abstract. The purpose of this article is to study the solvability of Barbashin-type integro-differential equation and initial value problem via the structure of well-known generalized convolutions. We give necessary and sufficient conditions for the unique explicit solution of this class of equations and estimate its boundedness in certain weighted \(L_1\) spaces. The illustrative examples of the obtained results are also considered.
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