In this paper we study the existence and uniqueness of solutions of a certain Fredholm type Riemann-Liouville integral equation of two variables by using Banach contraction principle.

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

In this paper, we will present composite boundary elements (CBE) for classical Fredholm boundary integral equations. These new boundary elements allow the low-dimensional discretisation of boundary integral equation where the minimal number of degrees of freedom is independent of the, possibly, huge number of charts which are necessary to describe a complicated surface. The applications are thr...

Fredholm integral equations arise naturally in the context of ordinary and partial differential equations: Two-point boundary value problems can be reformulated as Fredholm integral equations, whose kernels are continuous but have finite jump discontinuities in their derivatives. Two-dimensional elliptic boundary problems can be reformulated as Fredholm integral equations with kernels that have...

This paper involves extended b ? metric versions of a fractional differential equation, system equations and two-dimensional (2D) linear Fredholm integral equations. By various given hypotheses, exciting results are established in the setting an id="M2"> space. Thereafter, by making consequent use fixed point te...

Finite-dimensional perturbing operators are constructed using some incomplete information about eigen-solutions of an original and/or adjoint generalized Fredholm operator equation (with zero index). Adding such perturbing operator to the original one reduces the eigen-space dimension and can, particularly, lead to an unconditionally and uniquely solvable perturbed equation. For the second kind...

A method is used to solve the Fredholm–Volterra integral equation of the first kind in the space L2ðXÞ Cð0; T Þ, X 1⁄4 ðx; yÞ 2 X: ffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 þ y2 p n 6 a; z 1⁄4 0 o and T < 1: The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class Cð1⁄2X 1⁄2X Þ, while the kernel of the Volterra integral term is a positive an...