najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2024-15-4-448-456najo-35Research ArticleMATHEMATICSМАТЕМАТИКАThe Cauchy problem for a high-order wave equation with a loaded convolution type.Задача Коши для волнового уравнения высокого порядка с нагруженным типом сверткиhttps://orcid.org/0000-0001-7556-8942АгарвалП.AgarwalP.

Praveen Agarwal – Department of Mathematic Jaipur-30301

Non-linear Dynamics Research Center (NDRC) Ajman

goyal.praveen2011@gmail.comhttps://orcid.org/0000-0001-9687-5220БалтаеваУ.BaltaevaU.

Umida Baltaeva – Department of Exact science; Department of Applied Mathematics and Mathematical Physic

umida.baltayeva@mail.ruhttps://orcid.org/0000-0002-8387-6993МадрахимовУ.MadrakhimovU.

Umrbek Madrakhimov – Department of Applied Mathematics and Mathematical Physic

us.madrakhimov@gmail.comhttps://orcid.org/0009-0000-7438-1246БалтаевЖ. И.BaltaevJ. I.

Jamol I. Baltaev – Department of Technology

jamol.06@yahoo.comAnand International College of Engineerin; Ajman UniversityIndiaKhorezm Mamun Academy; Urgench State UniversityUzbekistanUrgench State UniversityUzbekistanRANCH University of TechnologyUzbekistan202431052025154448456Copyright © Agarwal P., Baltaeva U., Madrakhimov U., Baltaev J.I., 20252025Агарвал П., Балтаева У., Мадрахимов У., Балтаев Ж.И.Agarwal P., Baltaeva U., Madrakhimov U., Baltaev J.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/35

The present paper is devoted to the problem for one of the loaded wave integro-differential equations, which is equivalent to the nonlocal problem for a higher-order wave equation. The study aims at nonlocal problems and constructs a representation of the solution to the problem for an equation of hyperbolic type. Also, the paper provides examples of some cases where it will be possible to construct solutions to the problem explicitly and in the graphs.

Настоящая работа посвящена задаче для одного  нагруженного волнового интегро-дифференциального уравнения, которая эквивалентна решению нелокальной задачи для волнового уравнения высокого порядка. Исследование направлено на решение нелокальной задачи, и построению представления решения для уравнения гиперболического типа. Также в работе приведены примеры некоторых случаев, когда явно можно построить решение задачи в графах.

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The authors declare that there are no conflicts of interest present.