WSEAS Transactions on Heat and Mass Transfer
Print ISSN: 1790-5044, E-ISSN: 2224-3461
Volume 18, 2023
Problem of Determining the Density of Sources in a Multidimensional Heat Equation with the Caputo Time Fractional Derivative
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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.
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Keywords: Fractional heat equation, Robin boundary condition, Green’s function, Fox H- function, fundamental solution, direct problem, inverse problem, uniqueness
Pages: 90-98
DOI: 10.37394/232012.2023.18.9