Fractional Calculus in Russia at the End of XIX Century

Round 1

Reviewer 1 Report

In this paper, the authors study/reflect on the development of Fractional Calculus in Russia at the end of the XIX century, in particular, the results by Letnikov,  Sonine,  and Nekrasov. 

The subject is very interesting and presented some facts that were totally unknown to the Referee. This manuscript has novelty and presents important contributions for the community of Fractional Calculus. The Referee believes that history allows us to understand the present and project the future.

I suggest to the authors to make a revision of the English grammar and punctuation because there are some small misprints. For example, in "A. V.Letnikov" space is missing between "V." and the "Letnikov".

Author Response

Many thanks for your meaningful assessment of our manuscript.

Following your remarks we revise English grammer of the presentation.

Reviewer 2 Report

The present manuscript contains interesting information and material related to the theory of fractional calculus. It would be of interest to the journal readership. Therefore, the manuscript is appropriate for the journal.

 

Remark: in the Nekrasov Pavel Alekseevich short biography, page. 18, line 275, the year "1985" should be "1885".

Author Response

Many thanks for your kind words.

Following your remarks we revise English usage in the text.

Reviewer 3 Report

The manuscript presents a concise survey of the development of Fractional Calculus (FC) in Russia at the end of XIX century, with the emphasis on the works of Letnikov, Sonine and Nekrasov. Some of the results in the manuscript are presented for the first time in English. This work is a valuable contribution to the historical perspective on FC, giving credit to the Russian pioneers in this field. Therefore, it deserves to be published.

I have some minor technical remarks, concerning the style of the manuscript.

• On some places the text is not completely clear, e.g. the last sentence on p.1 (lines 19-20) is unclear; it is not clear how the “auxiliary functions” on p.3 (lines 61-63) are involved in the definition; the sentences on p. 17 (lines 233-235): maybe instead of “it” should be “he”?; 
• English grammar should be improved: for example, “we deals” should be “we deal”, “he try” should be “he tried” or “he tries”; “let the function is” should be “let the function be”;
• There are some misprints: on p.1 “Bernulli” should be “Bernoulli”, “Liouville’as” should be “Liouville’s”, “multiply integral” before eq. (13) should be “multiple integral”;
• Adding a section with Concluding remarks would be helpful for the reader;
• The style of the References is not the right style for this journal.

Author Response

Many thanks for the deep analysis of our manuscript.

1. We clarify presentation at certain places (including remarks on auxiliary functions).
2. We improved the English usage in the text.
3. Short Section "Conclusion" is added.
4. By recommendation of Academic Editor we use slightly different style of citation which we suppose to be more suitable to the reader than simply numbering of the items because of the length of the article and fairly large list of references.