Geodesic
New general solution to a nonlinear Fredholm integro-differential equation
Eurasian mathematical journal, Tome 10 (2019) no. 4, pp. 24-33

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Partition $\Delta_N$ of the interval $[0, T]$ into $N$ parts and introduction of additional parameters and new unknown functions on subintervals reduce a nonlinear Fredholm integro-differential equation to the special Cauchy problems for a system of nonlinear integro-differential equations with parameters. Conditions for the existence of a unique solution to the latter problem are obtained. Employing this solution we construct a $\Delta_N$ general solution to the nonlinear Fredholm integro-differential equation. Properties of the $\Delta_N$ general solution and its application to a nonlinear boundary value problem for the considered equation are discussed. 
@article{EMJ_2019_10_4_a3,
     author = {D. S. Dzhumabaev and S. T. Mynbayeva},
     title = {New general solution to a nonlinear {Fredholm} integro-differential equation},
     journal = {Eurasian mathematical journal},
     pages = {24--33},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2019_10_4_a3/}
}
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D. S. Dzhumabaev; S. T. Mynbayeva. New general solution to a nonlinear Fredholm integro-differential equation. Eurasian mathematical journal, Tome 10 (2019) no. 4, pp. 24-33. http://geodesic.mathdoc.fr/item/EMJ_2019_10_4_a3/