Tricomi type problem with integral conjugation condition for a mixed type equation with the hyper-bessel fractional  differential operator

Toshtemirov B H; Karimov E T

555

Name of journal“Matematika Instituti Byulleteni” elektron jurnali.
Number of editionMIB-2019-4
View count 555

Web Address https://drive.google.com/file/d/12cps2U5CWA6fJKC3JADn87_biB6jyIzH/view?usp=sharing

DOI

Date of creation in the UzSCI system 29-05-2021

Read count 553

Date of publication 16-09-2019

Main LanguageIngliz

Pages9-14

Tags

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.

Tags

aralash tipdagi tenglama

Trikomi tipidagi masala

integral ulash sharti

Giper-Bessel operatori

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.

Tags

уравнение смешанного типа

задача ти- па Трикоми

интегральное условие сопряжение

оператор гипер-Бесселя

№ Author name position Name of organisation

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

№ Name of reference

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.

Waiting

№	Author name	position	Name of organisation
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

№	Name of reference
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.