In 1982, Dubois and Prade [4, 5] first introduced the concept of integration of fuzzy functions. Kaleva [7] studied the measurability and integrability for the fuzzy set-valued mappings of a real variable whose values are normal, convex, upper semicontinuous, and compactly supported by fuzzy sets in Rn. Existence of solutions of fuzzy integral equations has been studied by several authors [1, 2...

In the present work‎, ‎a new stochastic algorithm is proposed to solve multiple dimensional Fredholm integral equations of the second kind‎. ‎The solution of the‎ integral equation is described by the Neumann series expansion‎. ‎Each term of this expansion can be considered as an expectation which is approximated by a continuous Markov chain Monte Carlo method‎. ‎An algorithm is proposed to sim...

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...

Using a parametric Riemann integral representation, a numerical algorithm for solving fuzzy Fredholm and Voltera integral equations of the second kind with arbitrary kernel is proposed and illustrated with examples. © 1999 Elsevier Science Inc. All rights reserved.

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...