In this paper we are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.

the main purpose of this article is to present an approximate solution for the two-dimensional nonlinear volterra integral equations using legendre orthogonal polynomials. first, the two-dimensional shifted legendre orthogonal polynomials are defined and the properties of these polynomials are presented. the operational matrix of integration and the product operational matrix are introduced. th...

In this paper we prove the existence and the uniqueness of the solutions of the Hammerstein-Volterra integral equation in the space of the absolutely continuous functions endowed with the bounded variation norm. After that, we find the resolvent of the corresponding linear integral equation in order to obtain a variation of parameters formula for the solutions of this linear equation. Finally, ...

In this paper, we apply Legendre wavelet collocation method to obtain the approximate solution of nonlinear Stratonovich Volterra integral equations. The main advantage of this method is that Legendre wavelet has orthogonality property and therefore coefficients of expansion are easily calculated. By using this method, the solution of nonlinear Stratonovich Volterra integral equation reduces to...

Second-kind Volterra integral equations with weakly singular kernels typically have solutions which are nonsmooth near the initial point of the interval of integration. Using an adaptation of the analysis originally developed for nonlinear weakly singular Fredholm integral equations, we present a complete discussion of the optimal (global and local) order of convergence of piecewise polynomial ...

In this paper, we establish some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two independent variables, and we present the applications to research the boundedness of solutions to retarded nonlinear Volterra-Fredholm type integral equations.

In this paper, we study the approximate solution of two-dimensional nonlinear Volterra integral equations by two-dimensional differential transform method. New theorems for the transformation of integrals are introduced and proved. We will give an applicable relation between the two-dimensional nonlinear Volterra integral equations and two-dimensional differential transformation, in order to so...

Abstract A new numerical method based on Haar wavelet is proposed for two-dimensional nonlinear Fredholm, Volterra and Volterra-Fredholm integral equations of first and second kind. The proposed method is an extension of the Haar wavelet method [1–3] from one-dimensional nonlinear integral equations (Fredholm and Volterra) to twodimensional nonlinear integral equations (Fredholm, Volterra and V...

In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.