On a generalization of the robin problem for the Laplace equation in the circle
129 91
Keywords:
Robin problem, fractional analog, Hadamard derivative, involutive transformation, uniqueness of solution, existence of solutionAbstract
In this paper, we study the solvability of the fractional analogue of the Robin
problem for the Laplace equation. A modified fractional differentiation operator in the sense of
Hadamard is considered as a boundary operator. Boundary conditions are given in the form of a
connection between different values of the unknown function in a circle. The problem is solved
using the Fourier expansion method. For various values of the parameters of the boundary operators
involved, theorems on the existence and uniqueness of a solution to the problem under study are
proved.
References
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Қожа Ахмет Ясауи атындағы Халықаралық қазақ-түрік университетінің хабарлары
(математика, физика, информатика сериясы), №3 (22), 2022
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REFERENCES
Hadamard J. Essai sur létude des fonctions données par leur développement de Taylor // Journal de Mathématiques Pures et Appliquées. – 1892. – Vol. 8. – P. 101 – 186.
Butzer P.L. , Kilbas A.A., Trujillo J.J. Compositions of Hadamard-type fractional integration operators and the semigroup property // Journal of Mathematical Analysis and Applications. – 2002. – Vol.269. – P.387-400.
Jarad F., Baleanu D., Abdeljawad A. Caputo-type modification of the Hadamard fractional derivatives // Advances in Difference Equations. – 2012. – Vol.2012, No.142. – P.1 – 8.
Kilbas A.A. Hadamard-type fractional calculus // Journal of the Korean Mathematical Society. – 2001. – Vol.38. – P.1191 – 1204 .
Kilbas A.A., Srivastava H.M, Trujillo J.J.Theory and applications of fractional differential equations.Elsevier, Amsterdam, 2006.
Arioua Y., Benhamidouche N. Boundary value problem for Caputo-Hadamard fractional differential equations //Surveys in Mathematics and its Applications. – 2017. – Vol.12. – P.103 – 115.
Boutiara A., Benbachir M., Guerbati K. Boundary value problem for nonlinear Caputo-Hadamard fractional differential equation with Hadamard fractional integral and anti-periodic conditions // Facta Universitatis Series Mathematics and Informatics. – 2021. – Vol. 36, No. 4. – P.735 – 748.
Turmetov B.Kh. On the solvability of some boundary value problems for the inhomogeneous polyharmonic equation with boundary operators of the Hadamard type // Differential Equations. – 2017. – V. 53, № 3. Р. 333–344.
Turmetov B.Kh., Koshanova M., Usmanov K. About solvability of some boundary value problems for Poisson equation in the ball conditions // Filomat . – 2018. –V. 32, No.3. – P. 939-946.
Evans LC. Partial differential equations. Vol. 19, Graduate studies in mathematics. Providence(RI): American Mathematical Society; 1998. 668 p.
Bisadze A.V., Samarskii A.A. O nekotoryh prosteishih obobsheniah lineinyh ellipticheskih kraevyh zadach [On some simplest generalizations of linear elliptic boundary value problems] // Doklady AN SSSR. – 1969. – Т.185, № 4. – С.739 – 740.
Przeworska-Rolewicz D. Some boundary value problems with transformed argument // Commentat. Math. – 1974. – V.17. – P.451 – 457.
Karachik V.V., Turmetov B.Kh. Solvability of one nonlocal Dirichlet problem for the Poisson equation // Novi Sad Journal of Mathematics. – 2020. – V. 50, No. 1. – P. 67 – 88.
Turmetov B. Kh., Karachik V.V. Solvability of nonlocal Dirichlet problem for
