Research Article

A solution to a nonlinear Fredholm integro-differential equation

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

DOI: 10.2989/16073606.2023.2183157

Author(s): Anar T. AssanovaInstitute of Mathematics and Mathematical Modeling MES RK, Kazakhstan, Sayakhat G. KarakenovaInstitute of Mathematics and Mathematical Modeling MES RK, Kazakhstan, Sandugash T. MynbayevaInstitute of Mathematics and Mathematical Modeling MES RK, Kazakhstan, Rosa E. UteshovaInstitute 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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Research Article

A solution to a nonlinear Fredholm integro-differential equation

Abstract

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