In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tych...

In this paper, a reliable iterative approach, for solving a wide range of linear and nonlinear Volterra-Fredholm integral equations is established. First the approach considers a discretized form of the integral terms where considering some conditions on the kernel of the integral equation it is proved that solution of the discretized form converges to the exact solution of the problem. Then th...

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

One of the modern applications of integral equations is the replacement of capital equipment under technological change. Corresponding models are known as vintage capital models (VCMs), see [1, 2, 3, 4, 5, 13, 14, 17]. They focus on optimization of the equipment lifetime and can be expressed via special Volterra integral equations with delay (e.g., Corduneanu [5]). Existing results about endoge...

A numerical method for solving nonlinear mixed Hammerstein integral equations is presented in this paper. The method is based upon hybrid of rationalized Haar functions approximations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. The Newton-Cotes nodes and Newton-Cotes integration method are then util...

The classical theory of optimal control deals with systems governed by ordinary differential equations or, in the case of discrete-time systems, finite difference equations. That basic theory has been extended in many directions: for example, we may have ssystems governed by partial differential equations, systems governed by sets of inequalities that involve partial derivatives, continuous-tim...

In this paper, we use the parametric form of fuzzy numbers, and aniterative approach for obtaining approximate solution for a classof fuzzy nonlinear Fredholm integral equations of the second kindis proposed. This paper presents a method based on Newton-Cotesmethods with positive coefficient. Then we obtain approximatesolution of the fuzzy nonlinear integral equations by an iterativeapproach.

In this study, we consider integral boundary value problems of nonlinear fractional differential equations with finite delay. Existence results positive solutions for the are obtained on basis Guo-Krasnoselskii theorem and Leggett-Williams fixed point theorem. Comprehensive examples follow main in respective sections.