AN INVERSE PROBLEM FOR A FRACTIONAL PARABOLIC EQUATION WITH INVOLUTION

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Published: iyl 11, 2023
Keywords:
differential equation with involution, Cauchy-Schwarz inequality, fractional integro-differentiation operator, Kaputo operator, Mittag-Leffler function.

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Бахтияр Кадиркулов
Ташкентский государственный университет востоковедения
Мухаммадали Жалилов
Fergana State University

Abstract

In this paper, we consider an inverse problem for a fourth-order fractional parabolic equation with a fractional Caputo operator and involution. Using the method of separation of variables, the solution to the problem is constructed in the form of a Fourier series. Theorems on the existence and uniqueness of a solution to the considered problem are proved. A criterion for the existence and uniqueness of a regular solution of the problem in a given domain is established.


Obtained results can be used in the study of boundary value problems for partial differential equations of fractional order, as well as in the theory of equations of mathematical physics.

Article Details

How to Cite
Кадиркулов, Б., & Жалилов, М. (2023). AN INVERSE PROBLEM FOR A FRACTIONAL PARABOLIC EQUATION WITH INVOLUTION. Scientific Journal of the Fergana State University, 28(3), 40. Retrieved from https://journal.fdu.uz/index.php/sjfsu/article/view/1878
Issue
No. 3 (2022): Scientific journal of the Fergana State University
Section
Mathematics
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Author Biographies

Бахтияр Кадиркулов, Ташкентский государственный университет востоковедения

Ташкентский государственный университет востоковедения, кафедра «Математика и информационные технологии»,доктор физико-математических наук, доцент.

Мухаммадали Жалилов, Fergana State University

Ферганский государственный университет, базовыйдокторант.

References

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