scholarly journals Fractional Calculus in Russia at the End of XIX Century

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1736
Author(s):  
Sergei Rogosin ◽  
Maryna Dubatovskaya
Keyword(s):  
Fractional Calculus ◽  
Survey Paper ◽  
Xix Century

In this survey paper, we analyze the development of Fractional Calculus in Russia at the end of the XIX century, in particular, the results by A. V. Letnikov, N. Ya. Sonine, and P. A. Nekrasov. Some of the discussed results are either unknown or inaccessible.

Mkhitar Djrbashian and his contribution to Fractional Calculus

2020 ◽  
Vol 23 (6) ◽  
pp. 1797-1809
Author(s):  
Sergei Rogosin ◽  
Maryna Dubatovskaya
Keyword(s):  
Cauchy Problem ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Approximation Theory ◽  
Fractional Derivatives ◽  
Complex Analysis ◽  
Integral Transforms ◽  
Modern Theory ◽  
Survey Paper ◽  
The Cauchy Problem

Abstract This survey paper is devoted to the description of the results by M.M. Djrbashian related to the modern theory of Fractional Calculus. M.M. Djrbashian (1918-1994) is a well-known expert in complex analysis, harmonic analysis and approximation theory. Anyway, his contributions to fractional calculus, to boundary value problems for fractional order operators, to the investigation of properties of the Queen function of Fractional Calculus (the Mittag-Leffler function), to integral transforms’ theory has to be understood on a better level. Unfortunately, most of his works are not enough popular as in that time were published in Russian. The aim of this survey is to fill in the gap in the clear recognition of M.M. Djrbashian’s results in these areas. For same purpose, we decided also to translate in English one of his basic papers [21] of 1968 (joint with A.B. Nersesian, “Fractional derivatives and the Cauchy problem for differential equations of fractional order”), and were invited by the “FCAA” editors to publish its re-edited version in this same issue of the journal.

Fractional derivatives and cauchy problem for differential equations of fractional order

2020 ◽  
Vol 23 (6) ◽  
pp. 1810-1836
Author(s):  
M.M. Dzherbashian ◽  
A.B. Nersesian
Keyword(s):  
Cauchy Problem ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Differential Operators ◽  
Editorial Note ◽  
Boundary Problems ◽  
Survey Paper ◽  
Constant Interest

Abstract Editorial Note: This is a paper by M.M. Djrbashian and A.B. Nersesian of 1968, that was published in Russian. There is a constant interest to Djrbashian’s contributions to the topic of fractional calculus and theory of Mittag-Leffler function. Unfortunately, his works were published in Russian and thus, are not easy accessible and not enough popular. Therefore, we invited hS. Rogosin and M. Dubatovskaya to prepare the survey paper in this same issue of “FCAA” and also to translate and edit the present paper in English. On behalf of Editorial Board and fractional calculus’ community, we express to them our thanks for this hard work, including also retyping, mentioning some typos, etc. Authors’ Summary: The concept of fractional integro-differentiation has found a number of applications in earlier papers of the present authors. With this paper we begin the publication of our results in the field of boundary problems for differential operators of fractional order.

Orthodox arrangement of the Pochaiv Lavra in the second third of the XIX century.

2021 ◽  
pp. 13-41
Author(s):  
Ella Volodymyrivna Bystrytska
Keyword(s):  
Local Level ◽  
The Political ◽  
Special Role ◽  
Economic Activities ◽  
Government Officials ◽  
Political Motivation ◽  
Archival Documents ◽  
The Status ◽  
The Russian Empire ◽  
Xix Century

Abstract: A series of imperial decrees of the 1820s ordering the establishment of a Greco-Uniate Theological Collegium and appropriate consistories contributed to the spread of the autocratic synodal system of government and the establishment of control over Greek Uniate church institutions in the annexed territories of Right-Bank Ukraine. As a result, the Greco-Uniate Church was put on hold in favor of the government's favorable grounds for the rapid localization of its activities. Basilian accusations of supporting the Polish November Uprising of 1830-1831 made it possible to liquidate the OSBM and most monasteries. The transfer of the Pochaiv Monastery to the ownership of the Orthodox clergy in 1831 was a milestone in the liquidation of the Greco-Uniate Church and the establishment of a Russian-style Orthodox mono-confessionalism. On the basis of archival documents, the political motivation of the emperor's decree to confiscate the Pochayiv Monastery from the Basilians with all its property and capital was confirmed. The transfer to the category of monasteries of the 1st class and the granting of the status of a lavra indicated its special role in strengthening the position of the autocracy in the western region of the Russian Empire. The orders of the Holy Synod outline the key tasks of ensuring the viability of the Lavra as an Orthodox religious center: the introduction of continuous worship, strengthening the personal composition of the population, delimitation of spiritual responsibilities, clarifying the affiliation of the printing house. However, maintaining the rhythm of worship and financial and economic activities established by the Basilians proved to be a difficult task, the solution of which required ten years of hard work. In order to make quick changes in the monastery, decisions were made by the emperor and senior government officials, and government agencies were involved at the local level, which required the coordination of actions of all parties to the process.

Small Industry, Gimmicks and Moscow Statistics, or How the Small Russian Enterprise Came into the World (Russian Physiological Sketch, 1830-1840)

2009 ◽  
pp. 123-129
Author(s):  
Yu. Golubitsky
Keyword(s):  
Small Businesses ◽  
Statistical Data ◽  
Russian Enterprise ◽  
Small Enterprises ◽  
Business Practices ◽  
Way Of Life ◽  
The World ◽  
Small Industry ◽  
Xix Century

The article considers business practices of Moscow small industry in the XIX century, basing upon physiological sketches of N. Polevoy and I. Kokorev, statistical data and the classification of professions are also presented. The author claims that the heroes of the analyzed sketches are the forefathers of Moscow small businesses and shows what a deep similarity their occupations and a way of life bear to the present-day routine existence of small enterprises.

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