Vestnik SamU. Estestvenno-Nauchnaya Ser., 2018, Issue 24, Issue 3, Pages 7–13
On fractional differentiation
S. O. Gladkov, S. B. Bogdanova
Department of Applied Software and Mathematical Methods, Moscow
Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, 125993, Russian Federation
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 $n = 1, 2…$, etc.
fractional differentiation, Fourier integral, Riemann integral, heat conduction, fractal, fractional dimension, Fourier equation, measure.
PDF file (228 kB)
http://www.journals.ssau.ru/.../6447 (published under the terms of the Creative Commons Attribution 4.0 International License)
S. O. Gladkov, S. B. Bogdanova, “On fractional differentiation”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 24:3 (2018), 7–13
Citation in format AMSBIB
\by S.~O.~Gladkov, S.~B.~Bogdanova
\paper On fractional differentiation
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|