We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.

In this paper, the existence and uniqueness of the solution of a nonlinear fully fuzzy implicit integro-differential equation arising in the field of fluid mechanics is investigated. First, an equivalency lemma is presented by which the problem understudy is converted to the two different forms of integral equation depending on the kind of differentiability of the solution. Then, the conditions...

Stefan problem with kinetics is reduced to a system of nonlinear Volterra integral equations of second kind and Newton's method is applied to linearize it. Product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. An example is provided to illustrated the applicability of the method.

The purpose of this note is to prove an abstract operator version of certain existence theorems for differential and Volterra integral equations which deal with stability properties of solutions. We will do this in such a way that the results unify, as well as generalize, many of the basic theorems concerning stability of such equations. Thus, our main result(Theorem2)is an abstract version of ...

Abstract In this paper, a new approach to the numerical solution of VolterraFredholm integral equations by using expansion method based on the composition of the inverse and direct discrete fuzzy transforms (shortly F-transforms) in combination with the collocation technique is proposed. First, the unknown function is approximated by using the composition of the inverse and direct discrete F-tr...

in this paper, a numerical efficient method based on two-dimensional block-pulse functions (bpfs) is proposed to approximate a solution of the two-dimensional linear stochastic volterra-fredholm integral equation. finally the accuracy of this method will be shown by an example.

in this paper we consider a nonlinear two-phase stefan problem in one-dimensional space. the problem is mapped into a nonlinear volterra integral equation for the free boundary.

In this paper, we propose a successive approximation method based on fuzzy wavelet like operator to approximate the solution of linear fuzzy Fredholm integral equations of the second kind with arbitrary kernels. We give the convergence conditions and an error estimate. Also, we investigate the numerical stability of the computed values with respect to small perturbations in the first iteration....

The integral model with finite memory is employed to analyze the timeline of COVID-19 epidemic in United Kingdom and government actions mitigate it. uses a realistic infection distribution. time-varying transmission rate determined from Volterra equation first kind. authors construct justify an efficient regularization algorithm for finding rate. are approbated on UK data several waves demonstr...