Summary: TEHRAN (FNA)- Engineers have designed a metamaterial device that can solve

integral equations. The device works by encoding parameters into the properties of an incoming electromagnetic wave; once inside, the device's unique structure manipulates the wave in such a way that it exits encoded with the solution to a pre-set

integral equation for that arbitrary input.

Consider the weakly singular Fredholm

integral equation of the second kind

An

integral equation is defined as an equation in which the unknown function [phi](x) to be determined appear under the integral sign.

Transformation of the original

integral equation taking into account the peculiarities of the magnetization of the core.

For the problem with periodic boundary conditions the

integral equation with Hilbert kernel is used [11]:

Consider the following fuzzy Fredholm

integral equation (38) with

Now, we represent the main theorem of this study, through which a weakly singular Volterra

integral equation can be expressed as a series of fractional differential transform for

Generally, these problems can be solved by an

integral equation using method of moments (MoM) [1] because it has lesser degrees of freedom than differential equation methods.

Many authors (e.g., [1-4]) introduced

integral equation methods for the two-dimensional Laplace equation solution in order to calculate the potential field.

(15) In the paper titled "Multiple Positive Solutions for Quadratic

Integral Equations of Fractional Order," the existence of multiple positive solutions for a class of quadratic

integral equation of fractional order was obtained by utilizing Avery-Henderson and Leggett-Williams multiple fixed-point theorems on cones.

Zajap, "Solvability of a functional

integral equation of fractional order in the class of functions having limits at infinity," Nonlinear Analysis: Theory, Methods & Applications, vol.

In this paper we prove the existence as well as approximation of the solutions of a certain generalized quadratic

integral equation with maxima via an algorithm based on successive approximations dveloped in Dhage iteration method under weak partial Lipschitz and compactness type conditions.