Vol. 6, №1, 2014
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FRACTALS AND FRACTIONAL CALCULUS IN PHYSICS


ESSAYS ON THE DEVELOPMENT OF FRACTIONAL CALCULUS IN THE A.V. LETNIKOV’S WORKS
Potapov A.A.
Dr Sci.Phys&Math, Chief Research Fellow, Academician of Russian Academy of Natural Sciences
Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, http://www.cplire.ru
11/7, Mokhovaya str., 125009 Moscow, Russian Federation
potapov@cplire.ru; www.potapov-fractal.com

Received 23.04.2012

The aim of the work is to rescue from oblivion the results to create a rigorous and complete theory of fractional calculus, obtained in the second half of the 19th century, the outstanding Russian mathematician and a patriot of Russia Alexei Vasilyevich Letnikov, a talented organizer of mathematical education in Russia and the founder of the School of Mathematics at the Moscow Higher Technical School (now Moscow State Technical Bauman University). His highest mathematical scholarship (on the basis of Moscow University and the Paris Ecole Polytechnique and the Sorbonne), impeccable honesty and integrity earned respect and love for young scientists, many of which played a prominent role in the history of Russian science. Represented by the main code of Letnikov’s works: master’s dissertation, well-known debate on the pages of Mathematics Collection of the Moscow mathematical society (now the journal of Russian Academy of Sciences), as well as his doctoral dissertation, completed a rationale of the fractional calculus - heritage, rescued from under the waters of Lethe long and painstaking work of the author of these essays. It also present a modern view of the early 21st century on this calculus, which is the only and necessary mathematical apparatus is rapidly evolving in the last decades, fractal physics. Also includes biographical materials, which demonstrate the personal nobility A.V. Letnikov and its beneficial effects on the mathematical thought and the scientific community in Russia.

Keywords: integrodifferentiation of fractional order, fractional operators, fractional calculus, fractals, fractal physics

UDC 537.86:519.22

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RENSIT, 2012, 4(1):3-102
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