Research Article

A solution to a nonlinear Fredholm integro-differential equation

Published in: Quaestiones Mathematicae
Volume 47 , issue 1 , 2024 , pages: 61–73

DOI: 10.2989/16073606.2023.2183157

Author(s): Anar T. Assanova Institute of Mathematics and Mathematical Modeling MES RK, Kazakhstan , Sayakhat G. Karakenova Institute of Mathematics and Mathematical Modeling MES RK, Kazakhstan , Sandugash T. Mynbayeva Institute of Mathematics and Mathematical Modeling MES RK, Kazakhstan , Rosa E. Uteshova Institute of Mathematics and Mathematical Modeling MES RK, Kazakhstan

Keywords: 34B15 , 34G20 , 45J05 , 47G20 , Nonlinear Fredholm integro-diﬀerential equations , special Cauchy problem , general solution , boundary value problem

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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.

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