ОБ ОДНОМ ОБОБЩЕНИИ ЗАДАЧИ РОБЕНА ДЛЯ УРАВНЕНИЯ ЛАПЛАСА В КРУГЕ
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Ключевые слова:
задача Робена, дробный аналог, производная Адамара, инволютивное преобразование, единственность решения, существование решенияАннотация
В настоящей работе исследуются вопросы разрешимости дробного аналога задачи Робена для уравнения Лапласа. В качестве граничного оператора рассматривается модифицированный оператор дробного дифференцирования в смысле Адамара. Краевые условия задаются в виде связи различных значений неизвестной функции в окружности. Задача решается с применением метода разложения Фурье. Для различных значений параметров участвующих в граничных операторов доказаны теоремы о существовании и единственности решения исследуемой задачи.
Библиографические ссылки
СПИСОК ИСПОЛЬЗОВАННОЙ ЛИТЕРАТУРЫ
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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 .
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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.
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Қожа Ахмет Ясауи атындағы Халықаралық қазақ-түрік университетінің хабарлары
(математика, физика, информатика сериясы), №3 (22), 2022
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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 generalized Helmholtz equation in a unit ball // Complex Variables and Elliptic Equations. – 2022. – P. 1 – 15.
Turmetov B.Kh., Nazarova K.Dz. On a generalization of the Neumann problem for the Laplace equation// Mathematische Nachrichten. – 2020. – V. 293,No. 1. – P.169 – 177.
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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
