B. I. Islomov, O. Kh. Abdullaev, “Gellerstedt type problem for the loaded parabolic-hyperbolic type equation with Caputo and Erdelyi-Kober operators of fractional order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 10, 33–46; Russian Math. (Iz. VUZ), 64:10 (2020), 29

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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, Number 10, Pages 33–46
DOI: https://doi.org/10.26907/0021-3446-2020-10-33-46 (Mi ivm9617)

This article is cited in 11 scientific papers (total in 11 papers)

Gellerstedt type problem for the loaded parabolic-hyperbolic type equation with Caputo and Erdelyi-Kober operators of fractional order

B. I. Islomov, O. Kh. Abdullaev

National University of Uzbekistan naimed after M.Ulugbek, 4 Universitetskaya str., Tashkent, 100174 Republic of Uzbekistan

Full-text PDF (387 kB) Citations (11)

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DOI: https://doi.org/10.26907/0021-3446-2020-10-33-46

Abstract: This work devoted to uniqueness and existence of solution of the local and non-local problems with integral gluing condition for the loaded parabolic-hyperbolic type equation involving Caputo derivatives which trace of solution involved into the Erdelyi-Kober integral operator. The uniqueness of solution is proved using by the method of integral energy. The existence of solution was proved by the method of integral equations.

Keywords: loaded equation, parabolic-hyperbolic type, Caputo derivatives, integral gluing condition, uniqueness and existence of solution, integral equations.

Received: 27.11.2019
Revised: 17.01.2020
Accepted: 29.06.2020

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, Volume 64, Issue 10, Pages 29–42
DOI: https://doi.org/10.3103/S1066369X20100047

Bibliographic databases:

Document Type: Article

UDC: 517.956

Language: Russian

Citation: B. I. Islomov, O. Kh. Abdullaev, “Gellerstedt type problem for the loaded parabolic-hyperbolic type equation with Caputo and Erdelyi-Kober operators of fractional order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 10, 33–46; Russian Math. (Iz. VUZ), 64:10 (2020), 29–42

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/ivm9617

https://www.mathnet.ru/eng/ivm/y2020/i10/p33

This publication is cited in the following 11 articles:

A. K. Urinov, D. M. Mirsaburova, “Gellerstedt–Moiseev Problem with Data on Parallel Characteristics in the Unbounded Domain for a Mixed Type Equation with Singular Coefficients”, Lobachevskii J Math, 45:3 (2024), 1318
O. Kh Abdullaev, “Nelokal'naya zadacha s integral'nym usloviem skleivaniya dlya nagruzhennogo parabolo-giperbolicheskogo uravneniya s drobnoy proizvodnoy Kaputo”, Differentsialnye uravneniya, 59:3 (2023), 350
O. Kh. Abdullaev, “A Nonlocal Problem with an Integral Matching Condition for a Loaded Parabolic-Hyperbolic Equation with a Fractional Caputo Derivative”, Diff Equat, 59:3 (2023), 351
Umida Baltaeva, Praveen Agarwal, Shaher Momani, “Extension of the Tricomi problem for a loaded parabolic–hyperbolic equation with a characteristic line of change of type”, Math Methods in App Sciences, 46:12 (2023), 12190
B. Zh. Kadirkulov, G. A. Kayumova, “Nelokalnaya zadacha dlya uravneniya smeshannogo tipa drobnogo poryadka s involyutsiei”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 210, VINITI RAN, M., 2022, 55–65
T. K. Yuldashev, T. G. Ergashev, T. A. Abduvahobov, “Nonlinear system of impulsive integro-differential equations with Hilfer fractional operator and mixed maxima”, Chelyab. fiz.-matem. zhurn., 7:3 (2022), 312–325
Praveen Agarwal, Umida Baltaeva, Nafosat Vaisova, “Cauchy problem for a parabolic–hyperbolic equation with non‐characteristic line of type changing”, Math Methods in App Sciences, 45:13 (2022), 8294
O. Kh. Abdullaev, A. A. Matchanova, “On a Problem for the Third Order Equation with Parabolic-Hyperbolic Operator Including a Fractional Derivative”, Lobachevskii J Math, 43:2 (2022), 275
U. Baltaeva, Y. Alikulov, I. I. Baltaeva, A. Ashirova, “Analog of the Darboux problem for a loaded integro-differential equation involving the Caputo fractional derivative”, Nanosyst.-Phys. Chem. Math., 12:4 (2021), 418–424
Akmaljon Abdullayev, Muyassar Hidoyatova, PROCEEDINGS OF THE III INTERNATIONAL CONFERENCE ON ADVANCED TECHNOLOGIES IN MATERIALS SCIENCE, MECHANICAL AND AUTOMATION ENGINEERING: MIP: Engineering-III – 2021, 2402, PROCEEDINGS OF THE III INTERNATIONAL CONFERENCE ON ADVANCED TECHNOLOGIES IN MATERIALS SCIENCE, MECHANICAL AND AUTOMATION ENGINEERING: MIP: Engineering-III – 2021, 2021, 070021
Muhammadali Jalilov, Gavhar Kayumova, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2365, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2021, 070010

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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