# of Applied Mathematics Scientific and Practical Conference Karshi state university 24-25 may, 2024 y. INITIAL-BOUNDARY VALUE PROBLEM ON -DIMENSIONAL TORUS FOR A TIMEFRACTIONAL SUBDIFFUSION EQUATION WITH AN ARBITRARY ELLIPTIC DIFFERENTIAL OPERATOR

## of Applied Mathematics Scientific and Practical Conference Karshi state university 24-25 may, 2024 y. INITIAL-BOUNDARY VALUE PROBLEM ON -DIMENSIONAL TORUS FOR A TIMEFRACTIONAL SUBDIFFUSION EQUATION WITH AN ARBITRARY ELLIPTIC DIFFERENTIAL OPERATOR

## Abstract

An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary

order elliptic differential operator is considered on -dimensional torus. Uniqueness and existence of

the classical solution of the posed problem are proved by the classical Fourier method. Sufficient

conditions for the initial function and for the right-hand side of the equation are indicated, under which

the corresponding Fourier series converge absolutely and uniformly.

## References

Pskhu, A.V.: Fractional partial differential equations (in Russian), M. NAUKA (2005)

Alimov, Sh.A., Ashurov, R.R., Pulatov, A.K.: Multiple Fourier Series and Fourier Integrals.

Commutative Harmonic Analysis, Springer, Berlin (1992)

## Published

2024-06-07

## How to Cite

*MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS*,

*1*(01). Retrieved from https://ojs.qarshidu.uz/index.php/mp/article/view/550

## Issue

## Section

Mathematical analysis, differential equations and equations of mathematical physics