Geodesic
Local displacement problem for equation of fractional diffusion
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 29 (2019) no. 4, pp. 28-34 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the fractional diffusion equation, we study a nonlocal boundary value problem of the first kind. The problem nonlocality is manifested in the fact that a linear combination of the values of the desired function is specified in the boundary condition. The theorem on the existence and uniqueness of a solution to the problem is proved.
Keywords: nonlocal boundary value problem, Riemann-Liouville fractional derivative, Wright type function.
Mots-clés : fractional diffusion equation 
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F. M. Losanova. Local displacement problem for equation of fractional diffusion. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 29 (2019) no. 4, pp. 28-34. http://geodesic.mathdoc.fr/item/VKAM_2019_29_4_a2/

[1] Nakhushev A. M., Uravneniya matematicheskoy biologii, Vyssh. shk., M., 1995, 301 pp., (in Russian)

[2] Bitsadze A. V., Samarskiy A. A., “O nekotorykh prosteyshikh obobshcheniyakh lineynykh ellipticheskikh krayevykh zadach”, Dokl. AN SSSR, 185:4 (1969), 739–740, (in Russian) | Zbl

[3] Losanova F. M., “Zadacha s usloviyem Samarskogo dlya uravneniya drobnoy diffuzii v polupolose”, Vestnik KRAUNTS. Fiz.-mat. nauki, 2015, no. 2(11), 17–21, (in Russian) | Zbl

[4] Kochubey A. N., Eydel'man S. D., “Zadacha Koshi dlya evolyutsionnykh uravneniy drobnogo poryadka”, Dokl. RAN, 394:2 (2004), 159–-161, (in Russian) | MR | Zbl

[5] Mainardi F., “Fractional relaxation-oscillation and fractional diffusion-wave phenomena”, Chaos Solitons Fractals, 1996, no. 7:9, 1461–-1477 | DOI | MR | Zbl

[6] Luchko Yu., Gorenflo R., “Scale-invariant solutions of a partial differential equation of fractional order”, Fract. Calc. Appl. Anal., 1:1 (1998), 63–-78 | MR | Zbl

[7] Andreyev A. A. , Yeremin A. S., “Krayevaya zadacha dlya uravneniya diffuzii s drobnoy proizvodnoy po vremeni”, Matematicheskoye modelirovaniye i krayevyye zadachi, Tr. dvenadtsatoy mezhvuz. konf., v. 3, SamGTU, Samara, 2004, 3-9, (in Russian)

[8] Pskhu A. V., “Resheniye krayevykh zadach dlya uravneniya diffuzii drobnogo poryadka metodom funktsii Grina”, Differentsial'nyye uravneniya, 39:10 (2003), 1430–1433, (in Russian) | MR | Zbl

[9] Pskhu A. V., “Resheniye pervoy krayevoy zadachi dlya uravneniya diffuzii drobnogo poryadka”, Differentsial'nyye uravneniya, 39:9 (2003), 1286–1289, (in Russian) | MR | Zbl

[10] Losanova F. M., “Zadacha s nelokal'nym smeshcheniyem dlya uravneniya drobnoy diffuzii”, Vestnik Samarskogo universiteta. Yestestvennonauchnaya seriya, 24:3 (2018), 35–40, (in Russian) | MR

[11] Nakhushev A. M., Zadachi so smeshcheniyem dlya uravneniya v chastnykh proizvodnykh, Nauka, M., 2006, 287 pp., (in Russian)

[12] Pskhu A. V., Uravneniya v chastnykh proizvodnykh drobnogo poryadka, Nauka, M., 2005, 199 pp., (in Russian)

[13] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnyye drobnogo poryadka i nekotoryye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987, 688 pp., (in Russian)

[14] Il'in V. A., Moiseyev Ye. I., “Nelokal'naya krayevaya zadacha dlya operatora Shturma-Liuvillya v differentsial'noy i raznostnoy traktovkakh”, Dokl. AN SSSR, 291:3 (1986), 534–538, (in Russian) | MR

[15] Il'in V. A., Moiseyev Ye. I., “Nelokal'naya krayevaya zadacha vtorogo roda dlya operatora Shturma-Liuvillya”, Differentsial'nyye uravneniya, 23:8 (1987), 1422–1431, (in Russian) | MR | Zbl