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 Vestnik SamU. Estestvenno-Nauchnaya Ser., 2020, Volume 26, Issue 1, Pages 14–22 (Mi vsgu621)

Mathematics

On the solution of some higher-order integro-differential equations of special form

E. Providas, I. N. Parasidis

University of Thessaly, Larissa, Greece

Abstract: The article is devoted to the solution of boundary value problems for higher-order linear integro-differential equations of Fredholm type with differential and integral operators encompassing powers of an ideal bijective linear differential operator whose inverse is known explicitly. The conditions for existence and uniqueness of solutions are derived and the solutions are delivered in closed form. The approach is based on the view that an integro-differential operator is a perturbed differential operator. The results obtained are of both theoretical and practical importance. The method is elucidated by solving two illustrative problems.

Keywords: integro-differential equations, initial value problems, boundary value problems, differential operators, power operators, composite products, exact solutions.

DOI: https://doi.org/10.18287/2541-7525-2020-26-1-14-22

Full text: PDF file (226 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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UDC: 629.7.05
Revised: 20.01.2020
Accepted:28.02.2020
Language:

Citation: E. Providas, I. N. Parasidis, “On the solution of some higher-order integro-differential equations of special form”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 26:1 (2020), 14–22

Citation in format AMSBIB
\Bibitem{ProPar20} \by E.~Providas, I.~N.~Parasidis \paper On the solution of some higher-order integro-differential equations of special form \jour Vestnik SamU. Estestvenno-Nauchnaya Ser. \yr 2020 \vol 26 \issue 1 \pages 14--22 \mathnet{http://mi.mathnet.ru/vsgu621} \crossref{https://doi.org/10.18287/2541-7525-2020-26-1-14-22}