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ANNALES Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae
Sectio Computatorica

Volumes » Volume 54 (2023)

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

Trinh Tuan

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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