A solution to a nonlinear Fredholm integro-differential equation

A. T. Assanova, Sayakhat G. Karakenova, Sandugash Mynbayeva, Roza E. Uteshova

2023

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DOI 10.2989/16073606.2023.2183157
Data confidence 85 high
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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.