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.

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In this paper, the Green functions of the first boundary-value problem for the fractional diffusion wave equation in multidimensional (bounded and unbounded) hyper-rectangular domains are constructed.
Mots-clés : diffusion wave equation
Keywords: Green function, fractional derivative, Dzhrbashyan–Nersesyan operator, boundary-value problem, Tikhonov condition.
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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