Voir la notice de l'article provenant de la source Math-Net.Ru
@article{INTO_2019_167_a6, author = {A. V. Pskhu}, title = {Green function of the first boundary-value problem for the fractional diffusion wave equation in a multidimensional rectangular domain}, journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory}, pages = {52--61}, publisher = {mathdoc}, volume = {167}, year = {2019}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/INTO_2019_167_a6/} }
TY - JOUR AU - A. V. Pskhu TI - Green function of the first boundary-value problem for the fractional diffusion wave equation in a multidimensional rectangular domain JO - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory PY - 2019 SP - 52 EP - 61 VL - 167 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/INTO_2019_167_a6/ LA - ru ID - INTO_2019_167_a6 ER -
%0 Journal Article %A A. V. Pskhu %T Green function of the first boundary-value problem for the fractional diffusion wave equation in a multidimensional rectangular domain %J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory %D 2019 %P 52-61 %V 167 %I mathdoc %U http://geodesic.mathdoc.fr/item/INTO_2019_167_a6/ %G ru %F INTO_2019_167_a6
A. V. Pskhu. Green function of the first boundary-value problem for the fractional diffusion wave equation in a multidimensional rectangular domain. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part III, Tome 167 (2019), pp. 52-61. http://geodesic.mathdoc.fr/item/INTO_2019_167_a6/
[1] Vagabov A. I., “Predstavlenie resheniya pervoi kraevoi zadachi dlya uravneniya teploprovodnosti v vide integralov Puassona i ikh prilozheniya”, Dokl. RAN., 375:4 (2000), 439–442 | MR | Zbl
[2] Voroshilov A. A., Kilbas A. A., “Zadacha Koshi dlya diffuzionno-volnovogo uravneniya s chastnoi proizvodnoi Kaputo”, Differ. uravn., 42:5 (2006), 599–609 | MR | Zbl
[3] Dzhrbashyan M. M., Nersesyan A. B., “Drobnye proizvodnye i zadachi Koshi dlya differentsialnykh uravnenii drobnogo poryadka”, Izv. akad. nauk Arm. SSR., 3:1 (1968), 3–28 | MR
[4] Kochubei A. N., “Diffuziya drobnogo poryadka”, Differ. uravn., 26:4 (1990), 660–670 | MR | Zbl
[5] Nakhushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003
[6] Pskhu A. V., “Reshenie kraevoi zadachi dlya uravneniya s chastnymi proizvodnymi drobnogo poryadka”, Differ. uravn., 39:8 (2003), 1092–1099 | MR | Zbl
[7] Pskhu A. V., “Fundamentalnoe reshenie diffuzionno-volnovogo uravneniya drobnogo poryadka”, Izv. RAN. Ser. mat., 73:2 (2009), 141–182 | DOI | MR | Zbl
[8] Pskhu A. V., “Pervaya kraevaya zadacha dlya drobnogo diffuzionno-volnovogo uravneniya v netsilindricheskoi oblasti”, Izv. RAN. Ser. mat., 81:6 (2017), 158–179 | DOI | MR | Zbl
[9] Pskhu A. V., Uravneniya v chastnykh proizvodnykh drobnogo poryadka, Nauka, M., 2005
[10] Pskhu A. V., “Reshenie pervoi kraevoi zadachi dlya uravneniya diffuzii drobnogo poryadka”, Differ. uravn., 39:9 (2003), 1286–1289 | MR | Zbl
[11] Pskhu A. V., “Reshenie kraevykh zadach dlya uravneniya diffuzii drobnogo poryadka metodom funktsii Grina”, Differ. uravn., 39:10 (2003), 1430–1433 | MR | Zbl
[12] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987
[13] Tarasov V. E., Modeli teoreticheskoi fiziki s integro-differentsirovaniem drobnogo poryadka, In-t komp. issled., M.–Izhevsk, 2011
[14] Agrawal O. P., “Solution for a fractional diffusion-wave equation defined in a bounded domain”, Nonlin. Dynam., 29:1 (2002), 145–155 | DOI | MR | Zbl
[15] Atanacković T. M., Pilipović S., Stanković B., Zorica D., Fractional Calculus with Applications in Mechanics, Wiley, London, 2014 | MR
[16] Eidelman S. D., Kochubei A. N., “Cauchy problem for fractional diffusion equations”, J. Differ. Equ., 199 (2004), 211–255 | DOI | MR | Zbl
[17] Fujita Ya., “Integrodifferential equation which interpolates the heat equation and the wave equation, I”, Osaka J. Math., 27:2 (1990), 309–321 | MR | Zbl
[18] Fujita Ya., “Integrodifferential equation which interpolates the heat equation and the wave equation, II”, Osaka J. Math., 27:4 (1990), 797–804 | MR | Zbl
[19] Gorenflo R., Iskenderov A., Luchko Yu., “Mapping between solutions of fractional diffusion-wave equations”, Fract. Calcul. Appl. Anal., 3:1 (2000), 75–86 | MR | Zbl
[20] Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations, North-Holland, Amsterdam, 2006 | MR | Zbl
[21] Mainardi F., “The fundamental solutions for the fractional diffusion-wave equation”, Appl. Math. Lett., 9:6 (1996), 23–28 | DOI | MR | Zbl
[22] Mainardi F., Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, World Scientific, Singapore, 2010 | MR | Zbl
[23] Miller K., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equation, Wiley, New York, 1993 | MR
[24] Oldham K., Spanier J., Fractional Calculus, Academic Press, New York, 1974 | MR | Zbl
[25] Podlubny I., Fractional Differential Equations, Academic Press, San Diego–New York–London, 1999 | MR | Zbl
[26] Schneider W. R., Wyss W., “Fractional diffusion and wave equations”, J. Math. Phys., 30:1 (1989), 134–144 | DOI | MR | Zbl
[27] Uchaikin V. V., Fractional Derivatives for Physicists and Engineers, Springer, Berlin–Beijing, 2013 | MR | Zbl
[28] Wright E. M., “On the coefficients of power series having exponential singularities”, J. London Math. Soc., 8:29 (1933), 71–79 | DOI | MR | Zbl
[29] Wright E. M., “The generalized Bessel function of order greater than one”, Quart. J. Math. Oxford Ser., 11 (1940), 36–48 | DOI | MR
[30] Wyss W., “The fractional diffusion equation”, J. Math. Phys., 27:11 (1986), 2782–2785 | DOI | MR | Zbl