@article{VMJ_2013_15_1_a4,
author = {M. A. Nazaraliev and V. D. Beibalaev},
title = {Dynamic systems described by two differential equations with derivatives of fractional order},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {30--40},
year = {2013},
volume = {15},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMJ_2013_15_1_a4/}
}
TY - JOUR AU - M. A. Nazaraliev AU - V. D. Beibalaev TI - Dynamic systems described by two differential equations with derivatives of fractional order JO - Vladikavkazskij matematičeskij žurnal PY - 2013 SP - 30 EP - 40 VL - 15 IS - 1 UR - http://geodesic.mathdoc.fr/item/VMJ_2013_15_1_a4/ LA - ru ID - VMJ_2013_15_1_a4 ER -
%0 Journal Article %A M. A. Nazaraliev %A V. D. Beibalaev %T Dynamic systems described by two differential equations with derivatives of fractional order %J Vladikavkazskij matematičeskij žurnal %D 2013 %P 30-40 %V 15 %N 1 %U http://geodesic.mathdoc.fr/item/VMJ_2013_15_1_a4/ %G ru %F VMJ_2013_15_1_a4
M. A. Nazaraliev; V. D. Beibalaev. Dynamic systems described by two differential equations with derivatives of fractional order. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 1, pp. 30-40. http://geodesic.mathdoc.fr/item/VMJ_2013_15_1_a4/
[1] Mandelbrot B. B., The Fractal Geometry of Nature, W. H. Freeman, New York, 1982, 468 pp. | MR | Zbl
[2] Olemskoi A. I., Flat A. Ya., “Ispolzovanie kontseptsii fraktala v fizike kondensirovannoi sredy”, Uspekhi fiz. nauk, 163:12 (1993), 1–50 | DOI
[3] Zosimov V. V., Lyamshev L. M., “Fraktaly v volnovykh protsessakh”, Uspekhi fiz. nauk, 165:4 (1995), 361–402 | DOI
[4] Samko S. G., Kilbas F. F., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye prilozheniya, Nauka i tekhnika, Minsk, 1987, 688 pp. | Zbl
[5] Nigmatulin R. I., “Drobnyi integral i ego fizicheskaya interpretatsiya”, Teoret. i mat. fizika, 90:3 (1992), 354–368 | MR | Zbl
[6] Chukbar K. V., “Stokhasticheskii perenos i drobnye proizvodnye”, Zhurn. eksperem. i teoret. fiziki, 108:5 (1995), 1875–1884
[7] Meilanov R. P., Yanpolov M. S., “Osobennosti fazovoi traektorii fraktalnogo ostsillyatora”, Pisma v zhurn. tekhn. fiziki, 28:1 (2002), 67–73
[8] Nakhushev A. M., Elementy drobnogo ischisleniya i ikh primenenie, Nalchik, 2003, 299 pp. | Zbl
[9] Nakhusheva V. A., Differentsialnye uravneniya matematicheskikh modelei nelokalnykh protsessov, Nauka, M., 2006, 174 pp. | MR | Zbl
[10] Andreev A. A., Ogorodnikov E. N., “Primenenie matrichnykh integro-differentsialnykh operatorov v reshenii zadachi Koshi dlya nekotorykh sistem obyknovennykh differentsialnykh uravnenii s proizvodnymi drobnogo poryadka”, Tr. VI Vseros. nauch. konf., Ch. 3, Samara, 2009, 31–38
[11] Beibalaev V. D., “Reshenie nachalnoi zadachi dlya differentsialnogo uravneniya fraktalnogo ostsillyatora”, Vestnik SamGTU. Ser. Fiz.-mat. nauki, 2009, no. 2(19), 240–242 | DOI
[12] Lefshets S., Geometricheskaya teoriya differentsialnykh uravnenii, Izd-vo inostr. lit-ry, M., 1961, 388 pp. | MR
[13] Andronov A. A., Leontovich E. A., Gordon I. I., Maier A. G., Kachestvennaya teoriya dinamicheskikh sistem, Nauka, M., 1966, 568 pp. | MR | Zbl
[14] Malinetskii G. G., Potapov A. B., Sovremennye problemy nelineinoi dinamiki, Editorial URSS, M., 2000, 336 pp.
[15] Bogolyubov N. N., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974, 504 pp. | MR
[16] Kheil Dzh., Kolebaniya v nelineinykh sistemakh, Mir, M., 1966, 230 pp.
[17] Moiseev N. N., Asimptoticheskie metody nelineinoi mekhaniki, Nauka, M., 1981, 400 pp. | MR | Zbl
[18] Veber V. K., “Struktura obschego resheniya sistemy $y^\alpha=Ay$, $0\alpha\leq1$”, Tr. Kirgiz. gos. un-ta. Ser. Mat. nauki, 1976, no. 11, 26–32 | Zbl
[19] Nazaraliev M. A., Beibalaev V. D., “Nelineinye kolebaniya v sredakh s fraktalnoi strukturoi”, Sb. tr. mezhdunar. Rossiisko-Bolgarskogo simpoziuma “Uravneniya smeshannogo tipa i rodstvennye problemy analiza i informatiki”, Nalchik–Khabez, 2010, 177–180
[20] Nazaraliev M. A., Meilanov R. P., Beibalaev V. D., Shabanova M. R., “Osobennosti fazovoi traektorii fraktalnogo ‘bryusselyatora’ ”, Sb. tr. VII Vseros. nauch. konf. s mezhdunar. uchastiem “Matematicheskoe modelirovanie i kraevye zadachi”, Ch. 3, Samara, 2010, 204–210
[21] Lavrova A. I., Postnikov E. B., Romanovskii Yu. M., “Bryusselyator – abstraktnaya khimicheskaya reaktsiya?”, Uspekhi fiz. nauk, 179:12 (2009), 1327–1332 | DOI