A solution to a nonlinear Fredholm integro-differential equation

Anar T. Assanova1 Institute of Mathematics and Mathematical Modeling MES RK, 050010, Almaty, Kazakhstan E-Mail [email protected]

Sayakhat G. Karakenova1 Institute of Mathematics and Mathematical Modeling MES RK, 050010, Almaty, Kazakhstan E-Mail [email protected];2 Al Farabi Kazakh National University, Almaty, 050040, Kazakhstan E-Mail [email protected]

Sandugash T. Mynbayeva1 Institute of Mathematics and Mathematical Modeling MES RK, 050010, Almaty, Kazakhstan E-Mail [email protected];3 K. Zhubanov Aktobe Regional University, Aktobe, 030000, KazakhstanCorrespondence[email protected]

Rosa E. Uteshova1 Institute of Mathematics and Mathematical Modeling MES RK, 050010, Almaty, Kazakhstan E-Mail [email protected];4 Department of Mathematical and Computer Modeling, International Information Technology University, 050034, Almaty, Kazakhstan. E-Mail [email protected]

Abstract

This paper deals with a Fredholm integro-diﬀerential equation with nonlinear integral term. By using the Dzhumabaev parametrization method, we reduce the equation to a special Cauchy problem and establish suﬃcient conditions for the existence of its unique solution. The solution to the special Cauchy problem is used to construct a new general solution to the Fredholm integro-diﬀerential equation. We investigate some properties of the new general solution and apply it to boundary value problems.

Mathematics Subject Classification (2020):

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A solution to a nonlinear Fredholm integro-differential equation

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A solution to a nonlinear Fredholm integro-differential equation

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