sg

Mathematics

No. 3 (2022): Scientific journal of the Fergana State University

AN INVERSE PROBLEM FOR A FRACTIONAL PARABOLIC EQUATION WITH INVOLUTION

Submitted
July 11, 2023
Published
2023-07-11

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.

References

  1. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and applications of fractional differential equations // North-Holland Mathematics studies, 204. Elsevier Science B. M., Amsterdam, 2006. xvi +523pp. ISBN -13:978-0-444-51832-3.
  2. Tarasov V.E. Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media // Publication City/Country Berlin, Germany. 2011. –505 p.
  3. Tenreiro Machado J.A. Handbook of Fractional Calculus with Applications; Walter de Gruyter GmbH: Berlin, Germany. -2019. Volumes 1-8. ISBN 978-3-11-057090-8.
  4. Sabitov K.B., Yunusova G. R. Inverse Problem for an Equation of Parabolic-Hyperbolic Type with a Nonlocal Boundary Condition // Differential Equations. 2012. Vol. 48, № 2. pp. 246–254.
  5. Тимошенко С.П., Янг Д.Х., Уивер У. Колебания в инженерном деле. -М.: Машиностроение. 1985. -472с.
  6. Jalilov M.A., Kayumova A.G. On a Boundary Value Problem for a Nonlocal Mixed-Type Equation with the Hilfer Operator //AIP Conference Proceedings. 2021. № 2365. 1-8 p.
  7. Кадиркулов Б.Ж., ЖалиловМ. А. Об одной краевой задаче для уравнения смешанного типа четвёртого порядка с дробной производной // Нелокальные краевые задачи и родственные проблемы математической биологии, информатики и физики. Международная конференция. 2021. Нальчик. № 4. С.89-90.