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Life and science of Alexey Gerasimov, one of the pioneers of fractional calculus in Soviet Union. (English) Zbl 1366.01058

Summary: 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.

MSC:

01A70 Biographies, obituaries, personalia, bibliographies
26-03 History of real functions
74-03 History of mechanics of deformable solids
26A33 Fractional derivatives and integrals
74D05 Linear constitutive equations for materials with memory

Biographic References:

Gerasimov, Alekseĭ N.
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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.; Caputo, M., Linear models of dissipation whose Q is almost frequency independent-II. Re-publ, Geophys. J. R. Astr. Soc.. Fract. Calc. Appl. Anal., 11, 1, 3-14 (2008) · Zbl 1210.65130
[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.; Gerasimov, A. N., The theory of the lever device for determination of the weight with a constant sensitivity (In Russian), Za obnovleniye textil’noy promyshlennosti, 7, 22-28 (1932)
[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).; Gerasimov, A. N., 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)
[4] A.N. Gerasimov, The problem of the springback and the internal friction (Russian). Prikladnaya Matematika i Mekhanika1, No 4 (1938), 493-536.; Gerasimov, A. N., The problem of the springback and the internal friction (Russian), Prikladnaya Matematika i Mekhanika, 1, 4, 493-536 (1938)
[5] A.N. Gerasimov, Letter to the Editor (Amendment to article, In Russian). Prikladnaya Matematika i Mekhanika2, No 1 (1938), 137.; Gerasimov, A. N., Letter to the Editor (Amendment to article, In Russian), Prikladnaya Matematika i Mekhanika, 2, 1, 137 (1938)
[6] A.N. Gerasimov, The bases of the theory of deformation of viscoelastic bodies (In Russian). Prikladnaya Matematika i Mekhanika2, No 3 (1938), 379-388.; Gerasimov, A. N., The bases of the theory of deformation of viscoelastic bodies (In Russian), Prikladnaya Matematika i Mekhanika, 2, 3, 379-388 (1938)
[7] A.N. Gerasimov, To the question of small oscillations of viscoelastic membranes (In Russian). Prikladnaya Matematika i Mekhanika2, No 4 (1939), 467-486.; Gerasimov, A. N., To the question of small oscillations of viscoelastic membranes (In Russian), Prikladnaya Matematika i Mekhanika, 2, 4, 467-486 (1939)
[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.; Gerasimov, A. N., Some of the Elasticity Problems in View of the After-Effect and Relaxation According to a Linear Law (1942)
[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 Mekhanika12, No 3 (1948), 251-260.; Gerasimov, A. N., Generalization of laws of the linear deformation and their application to problems of the internal friction (In Russian), Prikladnaya Matematika i Mekhanika, 12, 3, 251-260 (1948)
[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.; Gerasimov, A. N., Kinetics of the drawing process, I. Stationary process (In Russian), Izvestija of AN SSSR, Dept. of Technical Sciences, 12, 57-71 (1956)
[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.; Gerasimov, A. N., Kinetics of the drawing process, II. Unsteady process (In Russian), Izvestija of AN SSSR, Dept. of Technical Sciences, 5, 56-61 (1957)
[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.; Gerasimov, A. N., On speeds of the fibers during drawing (In Russian), Izvestija of AN SSSR, Det. of Technical Sciences, 5, 100-103 (1958)
[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.; Gerasimov, A. N., The quasi-stationary process of work of the drawing system (In Russian), Izvestija of AN SSSR, Dept. of Technical Sciences, 6, 118-119 (1958)
[14] A.Yu. Ishlinski, To the article of A.N. Gerasimov “The problem of the springback and iternal friction” (In Russian). Prikladnaya Matematika i Mekhanika3, No 2 (1939), 163-164.; Ishlinski, A. Yu., To the article of A.N. Gerasimov “The problem of the springback and iternal friction” (In Russian), Prikladnaya Matematika i Mekhanika, 3, 2, 163-164 (1939)
[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 Mekhanika4, No 1 (1940), 79-92.; Ishlinskii, A. Yu., The longitudinal vibrations of a rod in the presence of a linear law after-effect and relaxation (In Russian), Prikladnaya Matematika i Mekhanika, 4, 1, 79-92 (1940) · JFM 66.1374.04
[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).; <element-citation publication-type=”journal“ publication-format=”print”>Kilbas, A.A.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)
[17] J. Neumann, Allgemeine Eigenwerttheorie Hermitsescher Functional-operatoren. Math. Ann. 102 (1929), 49-131.; Neumann, J., Allgemeine Eigenwerttheorie Hermitsescher Functional-operatoren, Math. Ann., 102, 49-131 (1929) · JFM 55.0824.02
[18] I. Podlubny, Fractional Differential Equations. Academic Press, San Diego etc. (1999).; Podlubny, I., Fractional Differential Equations (1999) · Zbl 0918.34010
[19] V.S. Postnikov, Relaxation phenomena in metals and alloys subjected to deformation (In Russian). Uspekhi Fizicheskikh Nauk53 (1954), 87-108.; Postnikov, V. S., Relaxation phenomena in metals and alloys subjected to deformation (In Russian), Uspekhi Fizicheskikh Nauk, 53, 87-108 (1954) · Zbl 0059.22604
[20] I.I. Privalov, On the integral of the Cauchy-Stieltjes type (In Russian). Izvestija AN SSSR, Mathematics4, No 3 (1940), 61-276.; Privalov, I. I., On the integral of the Cauchy-Stieltjes type (In Russian), Izvestija AN SSSR, Mathematics, 4, 3, 61-276 (1940)
[21] Yu.N. Rabotnov, Equilibrium of an elastic medium with after-effect (In Russian). Prikladnaya Matematika i Mekhanika12, No 1 (1948), 53-62; Transl. in Engl. and Re-Publ. in: Fract. Calc. Appl. Anal. 17, No 3 (2014), 684-696; ; .; Rabotnov, Yu. N., Equilibrium of an elastic medium with after-effect (In Russian). Transl. in Engl. and Re-Publ, Prikladnaya Matematika i Mekhanika. Fract. Calc. Appl. Anal., 17, 3, 684-696 (2014) · Zbl 1306.74011 · doi:10.2478/s13540-014-0193-1
[22] F. Riesz, Sur la décomposition des opérations fonctionelles linéaires. Acta Sci. Math. Szeged4 (1928), 182-185.; Riesz, F., Sur la décomposition des opérations fonctionelles linéaires, Acta Sci. Math. Szeged, 4, 182-185 (1928) · JFM 55.0156.01
[23] F. Riesz, Über die linearen Transformationen des komplexen Hilbertschen Raumes. Sci. Math. Szeged5 (1930), 23-54.; Riesz, F., Über die linearen Transformationen des komplexen Hilbertschen Raumes, Sci. Math. Szeged, 5, 23-54 (1930) · JFM 56.0356.02
[24] F. Riss and B. Sz.-Nagy, Lectures on Functional Analysis (In Russian). Translated from French (Editor S.V. Fomin). 2nd Ed., “Mir” (1979).; Riss, F.; Sz.-Nagy, B., Lectures on Functional Analysis (In Russian), Translated from French (Editor S.V. Fomin) (1979)
[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 Mekhanika11, No 3 (1947), 329-338.; Rozovskii, M. I., 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, 3, 329-338 (1947) · Zbl 0030.08403
[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.; Rozovskii, M. I., 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, 3, 301-305 (1947)
[27] V.V. Uchaikin, Fractional Derivatives for Physicists and Engineers, Vol. I: Background and Theory, Vol. II: Applications. Springer, Heidelberg etc. (2013).; Uchaikin, V. V., Background and Theory. Applications, II (2013) · Zbl 1312.26002
[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; ; .; Valerio, D.; Machado, J. T.; Kiryakova, V., Historical Survey: Some pioneers of the applications of fractional calculus, Fract. Calc. Appl. Anal., 17, 2, 552-578 (2014) · Zbl 1305.26008 · doi:10.2478/s13540-014-0185-1
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