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 
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/
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[1] Gladkov S. O., Bogdanova S. B., “On fractional differentiation”, Vestnik of Samara University. Natural Science Series, 24:3 (2018), 7–13 (in Russian) | DOI | MR | Zbl

[2] Gladkov S. O., “On the theory of one-dimensional and quasi-one-dimensional thermal conductivity”, Technical Physics (Zhurnal Tekhnicheskoi Fiziki), 67:7 (1997), 8–12 (in Russian)

[3] Gladkov S. O., “On the theory of hydrodynamic phenomena in quasi-one-dimensional systems”, Technical Physics (Zhurnal Tekhnicheskoi Fiziki), 71:11 (2001), 130–132 (in Russian)

[4] Charles K. Chui, An Introduction to Wavelets, Mir, M., 2001, 412 pp. (in Russian)

[5] Dobeshi I., Ten Lectures on Wavelets, RKhD, Izhevsk, 2001, 464 pp. (in Russian)

[6] Mallat S., Wavelets in Signal Processing, Mir, M., 2005, 672 pp. (in Russian)

[7] Astaf'eva N. M., “Wavelet analysis: basic theory and some applications”, Physics-Uspekhi, 39:11 (1996), 1085–1108 | DOI | DOI

[8] Vorob'yev V. I., Gribunin V. G., Theory and practice of wavelet transform, VUS, SPb., 1999, 206 pp. (in Russian)

[9] Petukhov A. P., Introduction to Burst Basis Theory, SPbGTU, SPb., 1999, 132 pp. (in Russian)

[10] Koshlyakov N. S., Gliner E. B., Smirnov M. M., Partial differential equations of mathematical physics, Vysshaya shkola, M., 1970, 710 pp. (in Russian)