550

  • Ўқишлар сони 548
  • Нашр санаси 16-09-2019
  • Мақола тилиIngliz
  • Саҳифалар сони9-14
Калит сўзлар
Ўзбек

Ushbu maqolada xarakteristik uchburchak va to’g’ri
to’rtburchakdan tashkil topgan aralash sohada Giper-Bessel
kasr tartibli differensial operatori ishtirok etgan aralash tipdagi
tenglama uchun integral ko’rinishdagi ulash shartli chegaraviy
masalaning bir qiymatli yechilishi tadqiq qilingan. Olingan ilmiy
natija energiya integrallari va integral tenglamalar usullari bilan
isbotlangan.

Русский

В этой работе доказана однозначная разрешимость задачи
типа Трикоми с интегральным условием сопряжения для

уравнения смешанного типа с дробным оператором гипер-
Бесселя в смешанной области состоящая из характеристиче-
ского треугольника и прямоугольника. Полученный научный

результат доказан методами интеграл энергии и интеграль-
ных уравнений.

№ Муаллифнинг исми Лавозими Ташкилот номи
1 Toshtemirov B.H. Assistent-o'qituvchi Fergana Polytechnic Institute
2 Karimov E.T. Katta ilmiy hodim O'zR Fanlar akademiyasi V.I. Romanovskiy nomidagi Matematika instituti
№ Ҳавола номи
1 Uflyand, Y.S. On the question of the distribution of fluctuations in composite electrical lines. Injenerno- fizicheskiy jurnal 7(1), 1964, pp.89-92.
2 M. Gel’fand.Some questions of analysis and differential equations. Uspekhi Mat. Nauk Ser. 3 XIV, No. 87, 1959, pp. 3-19; Amer. Math. Soc. Transl. (2) 26, 1963. pp. 173-200.
3 T. D. Djuraev, A. Sopuev, and M. Mamajonov Boundary-value Problems for the Parabolic-hyperbolic Type Equations Tashkent: Fan, 1986.
4 Z.A.Nakhusheva. Nonlocal boundary value problems for main and mixed type differential equations Nalchik, 2011
5 G. Shashkov. System-structural Analysis of the Heat Exchange Processes and Its Application Moscow, 1983
6 Z.A.Nakhusheva. On the Tricomi Problem for the Lavrent’ev-Bitsadze Equation with a Nonlocal Transmission Condition. Differential equations. Vol. 41, No 10, 2005, pp. 1505-1508.
7 Dolgopolov, Mikhail V et al. Problems involving equations of hyperbolic type in the plane or three- dimensional space with conjugation conditions on a characteristic. Izvestiya: Mathematics 75(4), 2011, pp. 681-689.
8 E. T. Karimov, J. S. Akhatov. A boundary problem with integral gluing condition for a parabolic-hyperbolic equation involving the Caputo fractional derivative. Electronic Journal of Differential Equations. 14, 2014, pp. 1-6.
9 P. Agarwal, A. Berdyshev and E. Karimov. Solvability of a non-local problem with integral form transmitting condition for mixed type equation with Caputo fractional derivative. Results in Mathematics. 71(3), 2017, pp.1235-1257.
10 S. Kerbal, E. Karimov, N. Rakhmatullayeva. Non-local boundary problem with integral form transmitting condition for fractional mixed type equation in a composite domain. Mat. Model. Nat. Phenom. 12(3), 2017, pp. 95-104.
11 E. T. Karimov, A. S. Berdyshev, N. A. Rakhmatullayeva. Unique solvability of a non-local problem for mixed- type equation with fractional derivative. Mathematical Methods in the Applied Sciences. 40(8), 2017, pp. 2994-2999.
12 U. I. Baltaeva. On the solvability of boundary-value problems with continuous and generalized gluing conditions for the equation of mixed type with loaded term. Ukrainian Mathematical Journal, Vol. 69, No. 12, May, 2018, pp. 1845-1854.
13 Abdullaev O. Kh., Sadarangani K. Non-local problems with integral gluing condition for loaded mixed type equations involving the Caputo fractional derivative. Electronic Journal of Differential Equations, 2016(164), 2016, pp. 1-10.
14 Kadirkulov B.J. Boundary problems for mixed parabolic-hyperbolic equations with two lines of changing type and fractional derivative. Electronic Journal of Differential Equations, 2014(57), pp. 1-7.
15 Berdyshev A.S., Eshmatov B. E., Kadirkulov B.J. Boundary value problems for fourth-order mixed type equation with fractional derivative. Electronic Journal of Differential Equations, 2016(36), pp. 1-11.
16 E. T. Karimov. Tricomi type boundary value problem with integral conjugation condition for a mixed type equation with Hilfer fractional operator. Bulletin of the Institute of Mathematics. 1, 2019, pp. 19-26.
17 Fatma Al-Musalhi, Nasser Al-Salti and Erkinjon Karimov. Initial boundary value problems for fractional differential equation with hyper-Bessel operator. Fract. Calc. Appl. Anal., Vol. 21, No 1 (2018), pp. 200- 219, DOI: 10.1515/fca-2018-0013.
18 Podlubny I. Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution, Mathematics in Science and Engineering. Vol. 198. San Diego: Academic Press, 1999
19 Sobolev S. L. Partial Differential Equations of Mathematical Physics. Pergamon Press LTD, 1964.
20 Tricomi F. G. Integral Equations, New York: Dover Publ., 1985.
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