Geodesic
Boundary-value problems for loaded pseudoparabolic equations of fractional order and difference methods of their solving
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2019), pp. 3-12.

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The paper is devoted to local and nonlocal boundary-value problems for loaded differential equation with variable coefficients with Gerasimov–Kaputo fractional derivative. To solve the considered problems we obtain apriori estimates in differential and difference interpretations, from which it follows the uniqueness and stability of solution with respect to initial data and right-hand side, as well as convergence of solution to difference problem to a solution to differential problems.
Keywords: boundary-value problems, apriori estimate, loaded equations, differential equation of fractional order, Gerasimov–Kaputo fractional derivative.
Mots-clés : equation of pseudoparabolic type 
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M. Kh. Beshtokov. Boundary-value problems for loaded pseudoparabolic equations of fractional order and difference methods of their solving. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2019), pp. 3-12. http://geodesic.mathdoc.fr/item/IVM_2019_2_a0/

[1] Nakhushev A. M., “Nagruzhennye uravneniya i ikh prilozheniya”, Differents. uravneniya, 19:1 (1983), 86–94

[2] Kanchukoev V. Z., Kraevye zadachi dlya uravneniya tretego poryadka smeshannogo giperbolo-psevdoparabolicheskogo tipa, Diss. ... kand. fiz.-matem. nauk, M., 1984, 101 pp.

[3] Kanchukoev V. Z., “Kraevye zadachi dlya uravnenii psevdoparabolicheskogo i smeshannogo giperbolo-psevdoparabolicheskogo tipov i ikh prilozheniya k raschetu teplomassobmena v pochvogruntakh”, SAPR i ASPR v melioratsii, Nalchik, 1983

[4] Kochina N. I., “Voprosy regulirovaniya urovnya gruntovykh vod pri polivakh”, DAN SSSR, 213:1 (1973), 51–54 | Zbl

[5] Nakhushev A. M., Borisov V. N., “Kraevye zadachi dlya nagruzhennykh parabolicheskikh uravnenii i ikh prilozheniya k prognozu urovnya gruntovykh vod”, Differents. uravneniya, 13:1 (1977), 105–110 | Zbl

[6] Beshtokov M. Kh., “K kraevym zadacham dlya vyrozhdayuschikhsya psevdoparabolicheskikh uravnenii s drobnoi proizvodnoi Gerasimova–Kaputo”, Izv. vuzov. Matem., 2018, no. 10, 3–16 | Zbl

[7] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Minsk, 1987

[8] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1983

[9] Alikhanov A. A., “Apriornye otsenki reshenii kraevykh zadach dlya uravnenii drobnogo poryadka”, Differents. uravneniya, 46:5 (2010), 658–664 | Zbl

[10] Alikhanov A. A., “A new difference scheme for the time fractional diffusion equation”, J. Comput. Phys., 280 (2015), 424–438 | DOI | MR | Zbl

[11] Voevodin A. F., Shugrin S. M., Chislennye metody rascheta odnomernykh sistem, Nauka, SO AN SSSR, Novosibirsk, 1981 | MR