Geodesic
Uniqueness of the Solution of the Dirichlet Problem for a Multidimensional Differential Equation of Fractional Order
Matematičeskie zametki, Tome 109 (2021) no. 1, pp. 101-106.

Voir la notice de l'article provenant de la source Math-Net.Ru

A partial differential equation of fractional order with an arbitrary number of independent variables is studied. For integer orders of fractional derivatives, the equation under consideration becomes a second-order linear elliptic equation with Laplace operator in the principal part. The Dirichlet problem in a multidimensional domain is considered. The extremum principle for the equation under study and the uniqueness of the solution of the problem under consideration in a bounded or an unbounded domain are proved.
Keywords: conditionally elliptic equations, Riemann–Liouville fractional derivative, Dirichlet problem. 
@article{MZM_2021_109_1_a8,
     author = {O. Kh. Masaeva},
     title = {Uniqueness of the {Solution} of the {Dirichlet} {Problem} for a {Multidimensional} {Differential} {Equation} of {Fractional} {Order}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {101--106},
     publisher = {mathdoc},
     volume = {109},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a8/}
}
TY  - JOUR
AU  - O. Kh. Masaeva
TI  - Uniqueness of the Solution of the Dirichlet Problem for a Multidimensional Differential Equation of Fractional Order
JO  - Matematičeskie zametki
PY  - 2021
SP  - 101
EP  - 106
VL  - 109
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a8/
LA  - ru
ID  - MZM_2021_109_1_a8
ER  - 
%0 Journal Article
%A O. Kh. Masaeva
%T Uniqueness of the Solution of the Dirichlet Problem for a Multidimensional Differential Equation of Fractional Order
%J Matematičeskie zametki
%D 2021
%P 101-106
%V 109
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a8/
%G ru
%F MZM_2021_109_1_a8
O. Kh. Masaeva. Uniqueness of the Solution of the Dirichlet Problem for a Multidimensional Differential Equation of Fractional Order. Matematičeskie zametki, Tome 109 (2021) no. 1, pp. 101-106. http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a8/

[1] A. M. Nakhushev, Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003 | Zbl

[2] G. P. Lopushans'ka, “Fundamental boundary value problems for an equation in fractional derivatives”, Ukrainian Math. J., 51:1 (1999), 51–65 | DOI | MR

[3] M. Ferreira, N. Vieira, “Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators using Caputo derivatives”, Complex Var. Elliptic Equ., 62:9 (2017), 1237–1253 | DOI | MR | Zbl

[4] O. Kh. Masaeva, “Apriornaya otsenka dlya uravneniya s fraktalnym operatorom Laplasa v glavnoi chasti”, Dokl. Adygskoi (Cherkesskoi) Mezhdunar. AN, 11:1 (2009), 36–37

[5] O. Kh. Masaeva, “Printsip ekstremuma dlya fraktalnogo ellipticheskogo uravneniya”, Dokl. Adygskoi (Cherkesskoi) Mezhdunar. AN, 16:4 (2014), 31–35

[6] V. A. Nakhusheva, Differentsialnye uravneniya matematicheskikh modelei nelokalnykh protsessov, Nauka, M., 2006 | MR | Zbl

[7] O. Kh. Masaeva, “Zadacha Dirikhle dlya obobschennogo uravneniya Laplasa s proizvodnoi Kaputo”, Differents. uravneniya, 48:3 (2012), 442–446 | MR | Zbl

[8] O. Kh. Masaeva, “Zadacha Dirikhle dlya obobschennogo uravneniya Laplasa s drobnoi proizvodnoi”, Chelyabinskii fiz.-matem. zhurn., 2:4 (2017), 312–322

[9] O. Kh. Masaeva, “Zadacha neimana dlya obobschennogo uravneniya Laplasa”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2018, no. 3 (23), 83–90 | DOI | Zbl

[10] B. Kh. Turmetov, B. T. Torebek, “On solvability of some boundary value problems for a fractional analogue of the Helmholtz equation”, New York J. Math., 20 (2014), 1237–1251 | MR | Zbl

[11] Yu. Luchko, “Maximum principle for the generalized time-fractional diffusion equation”, J. Math. Anal. Appl., 351:1 (2009), 218–223 | DOI | MR | Zbl

[12] M. O. Mamchuev, “Analog printsipa Zaremby-Zhiro dlya uravneniya drobnoi diffuzii”, Dokl. Adygskoi (Cherkesskoi) Mezhdunar. AN, 12:2 (2010), 37–40

[13] A. M. Nakhushev, “Obratnye zadachi dlya vyrozhdayuschikhsya uravnenii i integralnye uravneniya Volterra tretego roda”, Differents. uravneniya, 10:1 (1974), 100–111 | MR | Zbl

[14] A. M. Nakhushev, Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995

[15] A. B. Pskhu, “O kraevoi zadache dlya uravneniya v chastnykh proizvodnykh drobnogo poryadka v oblasti s krivolineinoi granitsei”, Differents. uravneniya, 51:8 (2015), 1076–1082 | MR | Zbl

[16] A. B. Pskhu, “O prodolzhenii reshenii differentsialnogo uravneniya v chastnykh proizvodnykh drobnogo poryadka”, Differents. uravneniya, 50:1 (2014), 133–136 | MR | Zbl