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Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 8, Pages 27–41 (Mi ivm9266)  

This article is cited in 8 scientific papers (total in 8 papers)

On a method of solving the Cauchy problem for one-dimensional polywave equation with singular Bessel operator

Sh. T. Karimov

Fergana State University, 19 Murabbiylar str., Fergana, 150100 Republic Uzbekistan

Abstract: We study the Cauchy problem for an equation with singular Bessel operator. Unlike traditional methods to solve this problem, we apply Erdélyi–Kober fractional operator and find an explicit formula for the sought-for solution. We prove that the resulting formula is a unique classical solution to the problem.

Keywords: Cauchy problem, polywave equation, singular Bessel operator, Erdélyi–Kober operator.

Full text: PDF file (244 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:8, 22–35

Bibliographic databases:

UDC: 517.955
Received: 29.03.2016
Revised: 14.06.2016

Citation: Sh. T. Karimov, “On a method of solving the Cauchy problem for one-dimensional polywave equation with singular Bessel operator”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 8, 27–41; Russian Math. (Iz. VUZ), 61:8 (2017), 22–35

Citation in format AMSBIB
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\by Sh.~T.~Karimov
\paper On a method of solving the Cauchy problem for one-dimensional polywave equation with singular Bessel operator
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2017
\issue 8
\pages 27--41
\mathnet{http://mi.mathnet.ru/ivm9266}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2017
\vol 61
\issue 8
\pages 22--35
\crossref{https://doi.org/10.3103/S1066369X17080035}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85024855767}


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

    This publication is cited in the following articles:
    1. Sh.T. Karimov, “O nekotorykh obobscheniyakh svoistv operatora Erdeii–Kobera i ikh prilozheniya”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2017, no. 2(18), 20–40  mathnet  crossref  elib
    2. V. V. Katrakhov, S. M. Sitnik, “Metod operatorov preobrazovaniya i kraevye zadachi dlya singulyarnykh ellipticheskikh uravnenii”, Singulyarnye differentsialnye uravneniya, SMFN, 64, no. 2, Rossiiskii universitet druzhby narodov, M., 2018, 211–426  mathnet  crossref
    3. T. K. Yuldashev, “Nachalnaya zadacha dlya kvazilineinogo integro-differentsialnogo uravneniya v chastnykh proizvodnykh vysshego poryadka s vyrozhdennym yadrom”, Izv. IMI UdGU, 52 (2018), 116–130  mathnet  crossref  elib
    4. T. K. Yuldashev, K. Kh. Shabadikov, “Smeshannaya zadacha dlya nelineinogo psevdoparabolicheskogo uravneniya vysokogo poryadka”, Matematicheskii analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 156, VINITI RAN, M., 2018, 73–83  mathnet
    5. T. K. Yuldashev, K. Kh. Shabadikov, “Nachalnaya zadacha dlya kvazilineinogo differentsialnogo uravneniya v chastnykh proizvodnykh vysshego poryadka”, Matematicheskii analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 156, VINITI RAN, M., 2018, 106–116  mathnet
    6. T. K. Yuldashev, “Integro-differentsialnoe uravnenie s dvumernym operatorom Uizema vysokoi stepeni”, Matematicheskii analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 156, VINITI RAN, M., 2018, 117–125  mathnet
    7. T. K. Yuldashev, “Obratnaya kraevaya zadacha dlya integro-differentsialnogo uravneniya tipa Bussineska s vyrozhdennym yadrom”, Materialy mezhdunarodnoi nauchnoi konferentsii «Aktualnye problemy prikladnoi matematiki i fiziki» Kabardino-Balkariya, Nalchik, 17–21 maya 2017 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 149, VINITI RAN, M., 2018, 129–140  mathnet  mathscinet
    8. E. L. Shishkina, “Obschee uravnenie Eilera—Puassona—Darbu i giperbolicheskie $B$-potentsialy”, Uravneniya v chastnykh proizvodnykh, SMFN, 65, no. 2, Rossiiskii universitet druzhby narodov, M., 2019, 157–338  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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