Geodesic
To the question of fractional differentiation. Part~II
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 25 (2019) no. 3, pp. 7-11

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In the paper the investigation continues with the help of definition Fourier fractional differentiation setting in the previous paper “To the question of fractional differentiation”. There were given explicit expressions of a fairly wide class of periodic functions and for functions represented in the form of wavelet decompositions. It was shown that for the class of exponential functions all derivatives with non-integer exponent are equal to zero. The found derivatives have a direct relationship to practical problems and let them use to solve a large class of problems associated with the study of phenomena such as thermal conduction, transmissions, electrical and magnetic susceptibility for a wide range of materials with fractal dimensions.
Keywords: fractional differentiation, Fourier integral, Fourier's series, periodical functions, Gaussian exponent, exponential functions, numerical simulation.
Mots-clés : wavelet decompositions 
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     author = {S. O. Gladkov and S. B. Bogdanova},
     title = {To the question of fractional differentiation. {Part~II}},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
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S. O. Gladkov; S. B. Bogdanova. To the question of fractional differentiation. Part~II. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 25 (2019) no. 3, pp. 7-11. http://geodesic.mathdoc.fr/item/VSGU_2019_25_3_a0/