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Eurasian Mathematical Journal, 2019, Volume 10, Number 4, Pages 24–33
DOI: https://doi.org/10.32523/2077-9879-2019-10-4-24-33 (Mi emj345) 		 
This article is cited in 13 scientific papers (total in 13 papers)

New general solution to a nonlinear Fredholm integro-differential equation

D. S. Dzhumabaevab, S. T. Mynbayevabc

a International Information Technology University, 34A Dzhandossov St, 050034 Almaty, Kazakhstan
b Institute of Mathematics and Mathematical Modeling MES RK, 125 Pushkin St, 050010 Almaty, Kazakhstan
c K. Zhubanov Aktobe Regional State University, 34 Moldagulova Av, 030000, Aktobe, Kazakhstan
Full-text PDF (405 kB) Citations (13)
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DOI: https://doi.org/10.32523/2077-9879-2019-10-4-24-33
Abstract: Partition $\Delta_N$ of the interval $[0, T]$ into $N$ parts and introduction of additional parameters and new unknown functions on subintervals reduce a nonlinear Fredholm integro-differential equation to the special Cauchy problems for a system of nonlinear integro-differential equations with parameters. Conditions for the existence of a unique solution to the latter problem are obtained. Employing this solution we construct a $\Delta_N$ general solution to the nonlinear Fredholm integro-differential equation. Properties of the $\Delta_N$ general solution and its application to a nonlinear boundary value problem for the considered equation are discussed.
Keywords and phrases: nonlinear Fredholm integro-differential equation, special Cauchy problem, $\Delta_N$ general solution, boundary value problem.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP 05132486
This research is supported by the Ministry of Education and Science of the Republic Kazakhstan, Grant No. AP 05132486.
Received: 06.09.2019
Bibliographic databases:
Document Type: Article
MSC: 34B15, 34G20, 45J05, 47G20
Language: English
Citation: D. S. Dzhumabaev, S. T. Mynbayeva, “New general solution to a nonlinear Fredholm integro-differential equation”, Eurasian Math. J., 10:4 (2019), 24–33
Citation in format AMSBIB
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\by D.~S.~Dzhumabaev, S.~T.~Mynbayeva
\paper New general solution to a nonlinear Fredholm integro-differential equation
\jour Eurasian Math. J.
\yr 2019
\vol 10
\issue 4
\pages 24--33
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\crossref{https://doi.org/10.32523/2077-9879-2019-10-4-24-33}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85081999466}
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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