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Life And Science of Alexey Gerasimov, One of the Pioneers of Fractional Calculus in Soviet Union

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Abstract

Dedicated to the 120th anniversary of the birth of Alexey N. Gerasimov, one of the initiators of Fractional Calculus in Solid Mechanics.

In the first part of this survey we provide a brief sketch of his life. In the second part, the scientific contributions of the Soviet mechanician A.N. Gerasimov are reviewed.

Editorial Note. In a survey [28] recently published in this journal, Sect. 5, we the authors have mistaken the first name of Alexey Gerasimov with the incorrect name Andrey. This was due to unsuccessful attempts to find it unabbreviated in the available literature and by queries among colleagues. Some Internet sources (in Russian language) gave us the first name of another, also Soviet scientist in Mechanics. We do apologize for this fault.

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References

  1. M. Caputo, Linear models of dissipation whose Q is almost frequency independent-II. Geophys. J. R. Astr. Soc. 13 (1967), 529–539; Re-publ. in: Fract. Calc. Appl. Anal. 11, No 1 (2008), 3–14.

    Article  Google Scholar 

  2. A.N. Gerasimov, The theory of the lever device for determination of the weight with a constant sensitivity (In Russian). Za obnovleniye textil’noy promyshlennosti No 7 (1932), 22–28.

    Google Scholar 

  3. A.N. Gerasimov, The correspondence principle in the theory of linear operators (Graduated work on “Applied Mathematics”, Supervisor I.I. Privalov) (In Russian). Manuscript, Moscow State University, Fac. of Mech. and Math. (1936).

    Google Scholar 

  4. A.N. Gerasimov, The problem of the springback and the internal friction (Russian). Prikladnaya Matematika i Mekhanika 1, No 4 (1938), 493–536.

    Google Scholar 

  5. A.N. Gerasimov, Letter to the Editor (Amendment to article, In Russian). Prikladnaya Matematika i Mekhanika 2, No 1 (1938), 137.

    Google Scholar 

  6. A.N. Gerasimov, The bases of the theory of deformation of viscoelastic bodies (In Russian). Prikladnaya Matematika i Mekhanika 2, No 3 (1938), 379–388.

    Google Scholar 

  7. A.N. Gerasimov, To the question of small oscillations of viscoelastic membranes (In Russian). Prikladnaya Matematika i Mekhanika 2, No 4 (1939), 467–486.

    Google Scholar 

  8. A.N. Gerasimov, Some of the Elasticity Problems in View of the After-Effect and Relaxation According to a Linear Law. Thesis for the degree of a candidate of physical-mathematical sciences (In Russian). Manuscript, Moscow State University, 1942.

    Google Scholar 

  9. A.N. Gerasimov, Generalization of laws of the linear deformation and their application to problems of the internal friction (In Russian). Prikladnaya Matematika i Mekhanika 12, No 3 (1948), 251–260.

    Google Scholar 

  10. A.N. Gerasimov, Kinetics of the drawing process, I. Stationary process (In Russian). Izvestija of AN SSSR, Dept. of Technical Sciences No 12 (1956), 57–71.

    Google Scholar 

  11. A.N. Gerasimov, Kinetics of the drawing process, II. Unsteady process (In Russian). Izvestija of AN SSSR, Dept. of Technical Sciences No 5 (1957), 56–61.

    Google Scholar 

  12. A.N. Gerasimov, On speeds of the fibers during drawing (In Russian). Izvestija of AN SSSR, Det. of Technical Sciences No 5 (1958), 100–103.

    Google Scholar 

  13. A.N. Gerasimov, The quasi-stationary process of work of the drawing system (In Russian). Izvestija of AN SSSR, Dept. of Technical Sciences No 6 (1958), 118–119.

    Google Scholar 

  14. A.Yu. Ishlinski, To the article of A.N. Gerasimov “The problem of the springback and iternal friction” (In Russian). Prikladnaya Matematika i Mekhanika 3, No 2 (1939), 163–164.

    Google Scholar 

  15. A.Yu. Ishlinskii, The longitudinal vibrations of a rod in the presence of a linear law after-effect and relaxation (In Russian). Prikladnaya Matematika i Mekhanika 4, No 1 (1940), 79–92.

    Google Scholar 

  16. A.A. Kilbas, Theory and Applications of Differential Equations of Fractional Order (Course of Lectures, In Russian). Metodological School-Conference “Mathematical Physics and Nanotechnology” dedicated to the 40th anniversary of the revival of the University of Samara (Samara, 4-9 October 2009).

    Google Scholar 

  17. J. Neumann, Allgemeine Eigenwerttheorie Hermitsescher Functional-operatoren. Math. Ann. 102 (1929), 49–131.

    Article  Google Scholar 

  18. I. Podlubny, Fractional Differential Equations. Academic Press, San Diego etc. (1999).

    MATH  Google Scholar 

  19. V.S. Postnikov, Relaxation phenomena in metals and alloys subjected to deformation (In Russian). Uspekhi Fizicheskikh Nauk 53 (1954), 87–108.

    Article  Google Scholar 

  20. I.I. Privalov, On the integral of the Cauchy-Stieltjes type (In Russian). Izvestija AN SSSR, Mathematics 4, No 3 (1940), 61–276.

    Google Scholar 

  21. Yu.N. Rabotnov, Equilibrium of an elastic medium with after-effect (In Russian). Prikladnaya Matematika i Mekhanika 12, No 1 (1948), 53–62; Transl. in Engl. and Re-Publ. in: Fract. Calc. Appl. Anal. 17, No 3 (2014), 684–696; DOI: 10.2478/s13540-014-0193-1; https://www.degruyter.com/view/j/fca.2014.17.issue-3/issue-files/fca.2014.17.issue-3.xml.

    MathSciNet  Google Scholar 

  22. F. Riesz, Sur la décomposition des opérations fonctionelles linéaires. Acta Sci. Math. Szeged 4 (1928), 182–185.

    Google Scholar 

  23. F. Riesz, Über die linearen Transformationen des komplexen Hilbertschen Raumes. Sci. Math. Szeged 5 (1930), 23–54.

    MATH  Google Scholar 

  24. F. Riss and B. Sz.-Nagy, Lectures on Functional Analysis (In Russian). Translated from French (Editor S.V. Fomin). 2nd Ed., “Mir” (1979).

    Google Scholar 

  25. M.I. Rozovskii, Application of integral-differential equations to some dynamic problems of the theory of elasticity in the presence after-effect (In Russian), Prikladnaya Matematika i Mekhanika 11, No 3 (1947), 329–338.

    Google Scholar 

  26. M.I. Rozovskii, To the question on analytical description of deformation processes of constructions made with viscoelastic elements (In Russian). Izvestija of AN SSSR, Dept. of Technical Sciences No 3 (1947), 301–305.

    Google Scholar 

  27. V.V. Uchaikin, Fractional Derivatives for Physicists and Engineers, Vol. I: Background and Theory, Vol. II: Applications. Springer, Heidelberg etc. (2013).

  28. D. Valerio, J.T. Machado, V. Kiryakova, Historical Survey: Some pioneers of the applications of fractional calculus. Fract. Calc. Appl. Anal. 17, No 2 (2014), 552–578; DOI: 10.2478/s13540-014-0185-1; https://www.degruyter.com/view/j/fca.2014.17.issue-2/issue-files/fca.2014.17.issue-2.xml.

    Article  MathSciNet  Google Scholar 

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Correspondence to Olga G. Novozhenova.

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Novozhenova, O.G. Life And Science of Alexey Gerasimov, One of the Pioneers of Fractional Calculus in Soviet Union. FCAA 20, 790–809 (2017). https://doi.org/10.1515/fca-2017-0040

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  • DOI: https://doi.org/10.1515/fca-2017-0040

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