Alexandrovich I.M., Bondar O.S., Lyashko S.I., Lyashko N.I., Sydorov M.V.-S.
Integral operators that determine the solution of an iterated hyperbolic-type equation

Integral operators that translate arbitrary functions into regular solutions of a hyperbolic equation of 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 made it possible to present solutions of partial derivative equations in a form convenient for the analysis. Along the way, integral convolution equations with special functions in the kernel are solved. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: integral operator, iterated hyperbolic equations, mathematical induction, regular solutions, Convolution, Hyperbolic functions, Mathematical operators, Partial differential equations, Arbitrary functions, Convolution equations, Hyperbolic equations, Hyperbolic type, Integral operators, Partial derivative equations, Regular solution, Special functions, Integral equations

Cite:
Alexandrovich I.M., Bondar O.S., Lyashko S.I., Lyashko N.I., Sydorov M.V.-S. (2020). Integral operators that determine the solution of an iterated hyperbolic-type equation. Cybernetics and Systems Analysis, 56 (3), 70–79. doi: https://doi.org/10.1007/s10559-020-00256-3 http://jnas.nbuv.gov.ua/article/UJRN-0001121520 [In Ukrainian].