Abstract In this paper, the representation of the exact solution to the nonlinear Volterra-Fredholm integral equations will be obtained in the reproducing kernel space. The exact solution is represented in the form of series. Its approximate solution is obtained by truncating the series and a new numerical approximate method is obtained. The error of the approximate solution is monotone deceasi...

We apply the polynomial least squares method to obtain approximate analytical solutions for a very general class of nonlinear Fredholm and Volterra integro-differential equations. The is relatively simple straightforward one, but its precision this type equations high, fact that illustrated by numerical examples presented. comparison with previous approximations computed included test problems ...

One discrete problem of optimal population dynamics control with a controllable initial condition is considered. The process described by nonlinear system Fredholm-type difference equations. An analogue the L.S. Pontryagin’ maximum principle proved imposing series smoothness conditions on right side equation. linearized and Euler equation are for case convexity openness domain, which first-orde...

In this article, we prove the theorem concerning existence of solutions for some nonlinear integral equations. As an application, investigate problem Fredholm equations using technique relative compactness in conjunction with fixed point theorem. Our are placed space functions satisfying Hölder condition. work is more general than previous works [1-3]. last section, show efficiency approach on ...

osting by E Abstract Recently, Behiry et al. (in press) [8] have introduced a discretized version of the Adomian decomposition method, namely ‘‘Discrete Adomian Decomposition Method (DADM)’’, for solving nonlinear Fredholm integral equations. In this paper, we extent Behiry et al.’s idea on the wellknown homotopy analysis method, and introduce ‘‘Discrete homotopy analysis method (DHAM)’’. The o...

Some basic facts about Fredholm indices are briefly reviewed, often used in connection with Toeplitz and pseudodifferential operators, and which may be relevant for operators associated to fractals. Let H be a complex infinite-dimensional separable Hilbert space, which is of course unique up to isomorphism. Let B(H) be the Banach algebra of bounded linear operators on H, and let C(H) be the clo...

In the present work, we consider best proximal problem related to a coupled mapping, which define using control functions and weak inequalities. As consequence, obtain some results on fixed points. Our generalize recent in literature. Also, as an application of obtained, solution system Fredholm nonlinear integral equation. work is supported by several illustrations.