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@article{SEMR_2013_10_a41, author = {T. S. Aleroev}, title = {Boundary value problems for differential equations of fractional order}, journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a}, pages = {41--55}, publisher = {mathdoc}, volume = {10}, year = {2013}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a41/} }
T. S. Aleroev. Boundary value problems for differential equations of fractional order. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 41-55. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a41/
[1] A. V. Agibalova, “O polnote sistemy sobstvennykh i prisoedinennykh funktsii differentsialnykh operatorov poryadkov (2-$\varepsilon$) i (1-$\varepsilon$)”, Ukr. Mat. Vest., 7:2 (2010), 139–153 | MR
[2] A. V. Agibalova, “O polnote sistem kornevykh funktsii differentsialnogo operatora drobnogo poryadka s matrichnymi koeffitsientami”, Matematicheskie zametki, 88:2 (2010), 317–320 | DOI | MR | Zbl
[3] T. S. Aleroev, “Ob odnom klasse operatorov, svyazannykh s differentsialnymi uravneniyami drobnogo poryadka”, Sib. mat. zhurnal., 46:6 (2005), 1201–1207 | MR | Zbl
[4] T. S. Aleroev, “Zadacha Shturma–Liuvillya dlya differentsialnykh uravnenii drobnogo poryadka s drobnymi proizvodnymi v mladshikh chlenakh”, Dif. uravneniya, 18:2 (1982), 341–342 | MR | Zbl
[5] T. S. Aleroev, “O sobstvennykh znacheniyakh odnoi kraevoi zadachi dlya differentsialnogo uravneniya drobnogo poryadka”, Differents. uravneniya, 36:10 (2000), 1422–1423 | MR | Zbl
[6] T. S. Aleroev, Kraevye zadachi dlya differentsialnykh uravnenii s drobnymi proizvodnymi, Diss. ... doktora fiz.-mat. nauk, MGU, 2000
[7] T. Kato, Teoriya vozmuschenii lineinykh operatorov, «Mir», M., 1972 | Zbl
[8] T. S. Aleroev, “Kraevaya zadacha dlya differentsialnogo operatora drobnogo poryadka”, Dokl. Adygskoi (Cherkesskoi) Mezhdunar. AN, 1:1 (1994), 6–7
[9] Aleroev A. I., Aleroev T. S., “Ob odnom klasse polozhitelnykh operatorov, porozhdënnykh differentsialnymi vyrazheniyami drobnogo poryadka i kraevymi usloviyami Shturma–Liuvillya”, Izvestiya ChGPI, 1 (2009), 184–188
[10] T. S. Aleroev, H. T. Aleroeva, Ning-Ming Nie, Yi-Fa Tang, “Boundary Value Problems for Differential Equations of Fractional Order”, Mem. Differential Equations Math. Phys., 49 (2010), 21–82 | MR | Zbl
[11] M. M. Dzhrbaschyan, “Kraevaya zadacha dlya differentsialnogo operatora tipa Shturma–Liuvillya drobnogo poryadka”, Izv. Akad. nauk Armyanskoi SSR, seriya “Matematika”, 5 (1970), 71–96
[12] T. S. Aleroev, H. T. Aleroeva, “A problem on the zeros of the Mittag–Leffler function and the spectrum of a fractional-order differential operator”, Electron. J. Qual. Theory Differ. Equ., 25 (2009), 1–18 | MR
[13] A. Yu. Popov, “O kolichestve veschestvennykh sobstvennykh znachenii kraevoi zadachi dlya uravneniya vtorogo poryadka s drobnoi proizvodnoi”, Fundamentalnaya i prikladnaya matematika, 12 (2006), 137–155 | MR
[14] M. M. Dzhrbaschyan, A. B. Nersesyan, “Drobnye proizvodnye i zadacha Koshi dlya diffrenetsialnykh uravnenii drobnogo poryadka”, Izv. Akad. nauk Armyanskoi SSR, seriya «Matematika», 3:1 (1968), 3–29
[15] A. M. Gachaev, Kraevye zadachi dlya differentsialnykh uravnenii drobnogo poryadka, Dissertatsiya kandidata fiz.-mat. nauk, Nalchik, 2005
[16] I. K. Gokhberg, M. G. Krein, Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965 | MR
[17] I. K. Gokhberg, M. G. Krein, Teoriya volterrovykh operatorov v gilbertovom prostranstve, Nauka, M., 1967 | MR
[18] S. G. Samko, A. A. Kilbas, O. I. Marichev, Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987 | MR | Zbl
[19] M. A. Krasnoselskii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, V. Ya. Stetsenko, Priblizhennoe reshenie operatornykh uravnenii, Nauka, M., 1969 | MR
[20] F. Mainardi, “Fractional Relaxation-Oscillation and fractional Diffusion-wave Phenomena”, Chaos, Solitons and Fractals, 7:9 (1996), 1461–1477 | DOI | MR | Zbl
[21] M. M. Malamud, L. L. Oridoroga, “Analog teoremy Birkgofa i polnota rezultatov dlya differentsialnykh uravnenii drobnogo poryadka”, Ross. zhurnal. mat. fiz., 8:3 (2001), 287–308 | MR | Zbl
[22] M. M. Malamud, L. L. Oridoroga, “O nekotorykh voprosakh spektralnoi teorii obyknovennykh differentsialnykh uravnenii drobnogo poryadka”, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki, 9 (1998), 39–47 ; Journal of Mathematical Sciences, 174:4 (2011) | MR | Zbl
[23] M. M. Malamud, “Similarity of Volterra operators and related questions of the theory of differential equations of fractional order”, Trans. Moscow Math. Soc., 55 (1994), 57–122 | MR | Zbl
[24] N. M. Nie, Y. M. Zhao, S. Jimenez, M. Li, Y. F. Tang, L. Vazquez, “Solving two-point boundary value problems of fractional differential equations with Riemann–Liouville derivatives”, J. Syst. Simul., 22:1 (2010), 1–14 http://www.cc.ac.cn/2009research_report/0902.pdf
[25] P. Morse, H. Feshbach, Methods of theoretical physics, v. 2, New-York, 1953 | MR
[26] S. V. Erokhin, “Ob odnom klasse ostsillyatsionnykh matrits”, Matematika, informatika, estestvoznanie v ekonomike i v obschestve, MFYuA, Moskva, 2007, 13–16
[27] Yuan Chengjun, “Multiple positive solutions for $(n-1,1)$-type semipositone conjugate boundary value problems of nonlinear fractional differential equations”, E. J. Qualitative Theory of Diff. Equ., 36 (2010), 1–12 | DOI | MR | Zbl
[28] M. M. Dzhrbaschyan, Integralnye preobrazovaniya i predstavlenie funktsii v kompleksnoi oblasti, Nauka, M., 1966
[29] T. S. Aleroev, “O polnote sobstvennykh funktsii odnogo differentsialnogo operatora drobnogo poryadka”, Differents. uravneniya, 36:6 (2000), 829–830 | MR | Zbl
[30] T. S. Aleroev, B. I. Aleroev, “O sobstvennykh funktsiyakh odnogo nesamosopryazhennogo operatora”, Differents. uravneniya, 25:11 (1989), 1996–1997 | MR | Zbl
[31] T. S. Aleroev, “K probleme o nulyakh funktsii Mittag–Lefflera i spektre odnogo differentsialnogo operatora drobnogo poryadka”, Differents. uravneniya, 36:9 (2000), 1411–1415 | MR