DOI: 10.12732/ijam.v37i2.6
EXPLICIT SOLUTION OF TIME
FRACTIONAL NONLOCAL HEAT EQUATION
Yulian
T. Tsankov
Faculty of Mathematics and Informatics
Sofia University ”St. Kliment Ohridsky”
“J. Bouchier” Bul., No 5, Sofia - 1164, BULGARIA
Abstract. We study a one-dimensional fractional diffusion equation with the Caputo
time-derivative of order \mu \in (0, 1]. Applying spectral projectors, we find a series solution of the problem for a special choice of the initial function. Then, using operational calculus approach of Dimovski, we obtain an explicit representation of the solution in the general case. The expression obtained contains a non-classical convolution product of the particular solution and an arbitrary initial function. This result is an extension of the classical Duhamel principle, but for the space variable.
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to cite this paper?
DOI: 10.12732/ijam.v37i2.6
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 2
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