najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2023-14-5-511-517najo-287Research ArticleMATHEMATICSМАТЕМАТИКАBoundary value problem for a degenerate equation with a Riemann–Liouville operatorКраевая задача для вырождающегося уравнения с оператором Римана-Лиувилляhttps://orcid.org/0000-0001-7204-9127ИргашевБ. Ю.IrgashevB. Yu.

Bakhrom Yu. Irgashev

Namangan

bahromirgasev@gmail.comНаманганский инженерно-строительный институт, Институт математики имени В.И.Романовского Академии наук Республики УзбекистанNamangan Engineering Construction Institute; Institute of Mathematics named after V. I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan202308062025145511517Copyright © Irgashev B.Y., 20252025Иргашев Б.Ю.Irgashev B.Y.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/287

In the article, the uniqueness and solvability of one boundary value problem for a high-order equation with two lines of degeneracy with a fractional Riemann–Liouville derivative in a rectangular domain is studied by the Fourier method. Sufficient conditions for the well-posedness of the problem posed are obtained.

В статье методом Фурье исследуется единственность и разрешимость одной краевой задачи, в прямоугольной области, для уравнения высокого порядка с дробной производной Римана-Лиувилля с двумя линиями вырождения. Получены достаточные условия корректности поставленной задачи.

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