Geodesic
Dirchlet problem for a nonlocal wave equation with Riemann–Liouville derivative
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 27 (2019) no. 2, pp. 6-11
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The existence and uniqueness of the solution to Dirichlet problem for a second-order equation with a fractional derivative is proved. The equation under study is a wave equation for a integer value of the order of the fractional derivative.
Keywords: Dirichlet problem, Riemann–Liouville fractional derivative, Caputo fractional derivative, wave equation. 
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O. Kh. Masaeva. Dirchlet problem for a nonlocal wave equation with Riemann–Liouville derivative. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 27 (2019) no. 2, pp. 6-11. http://geodesic.mathdoc.fr/item/VKAM_2019_27_2_a0/

[1] Nakhushev A. M., Drobnoye ischisleniye i yego primeneniye, Fizmatlit, M., 2003, 272 pp.

[2] Pskhu A. B., Uravneniya v chastnykh proizvodnykh drobnogo poryadka, Nauka, M., 2005, 199 pp.

[3] Kerefov M. A., “Resheniye odnoy krayevoy zadachi dlya volnovogo uravneniya drobnogo poryadka”, Nelineynyye problemy differentsial'nykh uravneniy i matematicheskoy fiziki, Sb. nauchnykh trudov instituta matematiki NAN Ukrainy, Kiyev, 1997, 144-145

[4] Agrawal O. P., “Solution for a fractional diffusion-wave equation defined in a bounded domain”, Nonlinear Dynam, (29)-1:4 (2002), 145–155 | DOI | MR | Zbl

[5] Mainardi F., “The fundamental solutions for the fractional diffusion-wave equation”, Appl. Math. Lett., 9:6 (1996), 23–28. | DOI | MR | Zbl

[6] Pskhu A.V., “Fundamental'noye resheniye diffuzionno-volnovogo uravneniya drobnogo poryadka”, Izv. RAN, 73:2 (2009), 141-182 | MR | Zbl

[7] Masayeva O. KH., “Zadacha Dirikhle dlya nelokal'nogo volnovogo uravneniya”, Differents. uravneniya, 49:12 (2013), 1554-1559 | MR

[8] Masaeva O. Kh., “Necessary and sufficient conditions for the uniqueness od Dirichlet problem solution for nonlocal wave equation”, Bulletin KRASEC. Physical and Mathematical Sciences, 11:2 (2015), 19-23

[9] Dzhrbashyan M. M., Integral'nyye preobrazovaniya i predstavleniya funktsiy v kompleksnoy oblasti, Nauka, M., 1966, 672 pp.

[10] Pskhu A. V., “O veshchestvennykh nulyakh funktsii tipa Mittag-Lefflera”, Mat. zametki, 77:4 (2005), 592–599 | DOI | MR | Zbl

[11] Popov A. YU., “O kolichestve veshchestvennykh sobstvennykh znacheniy odnoy krayevoy zadachi dlya uravneniya vtorogo poryadka s drobnoy proizvodnoy”, Fundamental'naya i prikladnaya matematika, 12:6 (2006), 137–155

[12] Zorich V. A., Matematicheskiy analiz, v. II, Nauka, M., 1984, 640 pp. | MR