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Izv. Vyssh. Uchebn. Zaved. Mat., 2015, Number 9, Pages 74–79 (Mi ivm9038)  

This article is cited in 9 scientific papers (total in 9 papers)

Brief communications

On Fredholm partial integro-differential equation of the third order

T. K. Yuldashev

Chair of Higher Mathematics, Siberian State Aerospace University, 31 Krasnoyarskiy Rabochii Ave., Krasnoyarsk, 660014 Russia

Abstract: We study single-valued solvability of the initial value problem for a nonlinear partial Fredholm integro-differential equation of the third order with degenerate kernel. First we modify a method of degenerate kernel of partial Fredholm integro-differential equation of the second kind to the case of Fredholm integro-differential equations of the third order. After solving the corresponding system of algebraic equations we obtain the Volterra integral equation of the second kind. Further we use the method of successive approximations combined with the method of contractive mappings.

Keywords: initial value problem, integro-differential equation, Fredholm equation with degenerate kernel, algebraic system of equations, single-valued solvability.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:9, 62–66

Document Type: Article
UDC: 517.95
Presented by the member of Editorial Board: R. B. Salimov
Received: 23.12.2014

Citation: T. K. Yuldashev, “On Fredholm partial integro-differential equation of the third order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 9, 74–79; Russian Math. (Iz. VUZ), 59:9 (2015), 62–66

Citation in format AMSBIB
\by T.~K.~Yuldashev
\paper On Fredholm partial integro-differential equation of the third order
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2015
\issue 9
\pages 74--79
\jour Russian Math. (Iz. VUZ)
\yr 2015
\vol 59
\issue 9
\pages 62--66

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    This publication is cited in the following articles:
    1. 53, no. 1, 2017, 99–108  crossref  isi
    2. T. K. Yuldashev, “Nelineinoe integro-differentsialnoe uravnenie psevdoparabolicheskogo tipa s nelokalnym integralnym usloviem”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 1(32), 11–23  mathnet  crossref
    3. T. K. Yuldashev, “Smeshannoe differentsialnoe uravnenie tipa Bussineska”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2016, no. 2(33), 13–26  mathnet  crossref
    4. T. K. Yuldashev, “Nonlocal problem for a mixed type differential equation in rectangular domain”, Uch. zapiski EGU, ser. Fizika i Matematika, 2016, no. 3, 70–78  mathnet
    5. T. K. Yuldashev, “Obratnaya zadacha dlya obyknovennogo integro-differentsialnogo uravneniya s vyrozhdennym yadrom i nelokalnymi integralnymi usloviyami”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2016, no. 3, 19–33  mathnet  crossref  elib
    6. T. K. Yuldashev, “Obyknovennoe integro-differentsialnoe uravnenie s vyrozhdennym yadrom i integralnym usloviem”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:4 (2016), 644–655  mathnet  crossref  zmath  elib
    7. T. K. Yuldashev, “Nelokalnaya kraevaya zadacha dlya neodnorodnogo psevdoparabolicheskogo integro-differentsialnogo uravneniya s vyrozhdennym yadrom”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 1(38), 42–54  mathnet  crossref
    8. T. K. Yuldashev, “Ob odnoi nelokalnoi zadache dlya neodnorodnogo integro-differentsialnogo uravneniya tipa Bussineska s vyrozhdennym yadrom”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 159, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2017, 88–99  mathnet  mathscinet  elib
    9. T. K. Yuldashev, “Determination of the coefficient and boundary regime in boundary value problem for integro-differential equation with degenerate kernel”, Lobachevskii J. Math., 38:3, SI (2017), 547–553  crossref  mathscinet  zmath  isi  scopus
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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