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.