TO THE QUESTION OF FRACTIONAL DIFFERENTIATION. PART II


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Abstract

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.

About the authors

S. O. Gladkov

Moscow Aviation Institute (National Research University)

Author for correspondence.
Email: morenov@ssau.ru
ORCID iD: 0000-0002-2755-9133

Doctor of Physical and Mathematical Sciences, professor, professor of the Department of Applied Software and Mathematical Methods

S. B. Bogdanova

Moscow Aviation Institute (National Research University)

Email: morenov@ssau.ru

Candidate of Physical and Mathematical Sciences, assistant professor, assistant professor of the Department of Applied Software and Mathematical Methods

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Copyright (c) 2020 С. О. Гладков, С. Б. Богданова

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