**DOI: ****10.12732/ijam.v37i2.6
**

** **

**EXPLICIT
SOLUTION OF TIME**

**FRACTIONAL
NONLOCAL HEAT EQUATION**

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**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.

**How
to cite this paper?**

**DOI: 10.12732/ijam.v3****7****i2.****6****
Source: **International Journal of Applied Mathematics

**References**

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