Problem of Determining the Density of Sources in a Multidimensional Heat Equation with the Caputo Time Fractional Derivative-Reference-Cited by-同舟云学术

Problem of Determining the Density of Sources in a Multidimensional Heat Equation with the Caputo Time Fractional Derivative

Published:2023-12-05 Issue: Volume:18 Page:90-98
ISSN:2224-3461
Container-title:WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER
language:en
Short-container-title:1790-5044

Author:

Durdiev Durdimurod¹

Affiliation:

1. Bukhara Branch of Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, UZBEKISTAN

Abstract

In this paper, we propose a new formula for representing the solution of the third initial-boundary value problem for multidimensional fractional heat equation with the Caputo derivative. This formula is obtained by the continuation method used in the theory of partial differential equations with integer derivatives. The Green’s function of the problem is also constructed in terms of the Fox H- function. Involving the results of solving a direct problem and the overdetermination condition, a uniqueness theorem for the definition of the spatial part of the multidimensional source function is proved.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

General Physics and Astronomy

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