A solution to a nonlinear Fredholm integro-differential equation
Assanova A.T. Karakenova S.G. Mynbayeva S.T. Uteshova R.E.
2024Taylor and Francis Ltd.
Quaestiones Mathematicae
2024#47Issue 161 - 73 pp.
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.
boundary value problem , general solution , Nonlinear Fredholm integro-differential equations , special Cauchy problem
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Institute of Mathematics and Mathematical Modeling MES RK, Almaty, 050010, Kazakhstan
Al Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Department of Mathematical and Computer Modeling, International Information Technology University, Almaty, 050034, Kazakhstan
Institute of Mathematics and Mathematical Modeling MES RK
Al Farabi Kazakh National University
Department of Mathematical and Computer Modeling
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