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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 517. 95
I.M. Alexandrovich1, O.S. Bondar2, S.I. Lyashko3, N.I. Lyashko4, M.V.-S. Sydorov5


1 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

ialexandrovich@ukr.net

2 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

alenkajob@gmail.com

3 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

lyashko.serg@gmail.com

4 V.M. Glushkov Institute of Cybernetics, National Academy
of Sciences of Ukraine, Kyiv, Ukraine

lyashko.natali@gmail.com

5 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

myksyd@knu.ua

INTEGRAL OPERATORS THAT DETERMINE THE SOLUTION
OF AN ITERATED HYPERBOLIC-TYPE EQUATION

Abstract. Integral operators that translate arbitrary functions into regular solutions of the hyperbolic equation of the second and higher orders are constructed. The Cauchy problem for the fourth-order hyperbolic equation is solved. The use of the theory of special functions helped us to obtain the image of solutions of partial derivative equations in a form convenient for the analysis. Along the way, solvable integral equations with special functions in the kernel are solved.

Keywords: integral operator, hyperbolic type iterated equations, regular solutions, mathematical induction.



FULL TEXT

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