Geodesic
On fractional differentiation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 3, pp. 7-13

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Due to the operation of fractional differentiation introduced with the help of Fourier integral, the results of calculating fractional derivatives for certain types of functions are given. Using the numerical method of integration, the values of fractional derivatives for arbitrary dimensionality $\varepsilon$, (where $\varepsilon$ is any number greater than zero) are calculated. It is proved that for integer values of $\varepsilon$ we obtain ordinary derivatives of the first, second and more high orders. As an example it was considered heat conduction equation of Fourier, where spatial derivation was realized with the use of fractional derivatives. Its solution is given by Fourier integral. Mmoreover, it was shown that integral went into the required results in special case of the whole $\varepsilon$ obtained in $n$-dimensional case, where $n = 1, 2\dots$, etc.
Keywords: fractional differentiation, Fourier integral, Riemann integral, heat conduction, measure.
Mots-clés : fractal, fractional dimension, Fourier equation 
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     author = {S. O. Gladkov and S. B. Bogdanova},
     title = {On fractional differentiation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {7--13},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2018_24_3_a0/}
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S. O. Gladkov; S. B. Bogdanova. On fractional differentiation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 3, pp. 7-13. http://geodesic.mathdoc.fr/item/VSGU_2018_24_3_a0/