The Volterra delay integral equations have numerous applications in various branches of science, including biology, ecology, physics and modeling of engineering and natural sciences. In many cases, it is difficult to obtain analytical solutions of these equations. So, numerical methods as an efficient approximation method for solving Volterra delay integral equations are of interest to many res...

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...

In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied.

In this brief note,  using the technique of measures of noncompactness, we give some extensions of Darbo fixed point theorem. Also we prove  an existence result for a quadratic  integral equation of Hammerstein type on an unbounded interval in two variables  which includes several classes of nonlinear integral equations of Hammerstein type. Furthermore, an example is presented to show the effic...