Here, the solution in one, two and three dimensional for the Volterra–Fredholm integral equation of the first kind is obtained in the space L2ðXÞ C1⁄20; T , T < 1. Using a numerical method the integral equation of Volterra–Fredholm becomes a linear system of Fredholm integral equation when that the kernel of Fredholm integral takes a logarithmic form, Carleman function, generalized potential fu...

In this paper, we propose a successive approximation method based on fuzzy wavelet like operator to approximate the solution of linear fuzzy Fredholm integral equations of the second kind with arbitrary kernels. We give the convergence conditions and an error estimate. Also, we investigate the numerical stability of the computed values with respect to small perturbations in the first iteration....

In this paper a linear Fuzzy Fredholm Integral Equation(FFIE) with arbitrary Fuzzy Function input and symmetric triangular (Fuzzy Interval) output is considered. For each variable, output is the nearest triangular fuzzy number (fuzzy interval) to the exact fuzzy solution of (FFIE).

In this paper we intend to offer new numerical methods to solvethe fuzzy Fredholm- Volterra integral equations of the firstkind $(FVFIE-1)$. Some examples are investigated to verify convergence results and to illustrate the efficiently of the methods.  

In this paper an expansion method, based on Legendre or any orthogonal polynomials, is developed to find numerical solutions of two-dimensional linear Fredholm integral equations. We estimate the error of the method, and present some numerical examples to demonstrate the accuracy of the method. 2000 Mathematics subject classification: 65R20.

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 article, a numerical method based on  improvement of block-pulse functions (ibpfs) is discussed for solving the system of linear volterra and fredholm integral equations. by using ibpfs and their operational matrix of integration, such systems can be reduced to a linear system of algebraic equations. an efficient error estimation and associated theorems for the proposed method are also ...

In this paper, existence theorems for the fuzzy Volterra-Fredholm integral equations of mixed type (FVFIEMT) involving fuzzy number valued mappings have been investigated. Then, by using Banach's contraction principle, sufficient conditions for the existence of a unique solution of FVFIEMT are given. Finally, illustrative examples are presented to validate the obtained results.

Fuzzy integral equations play major roles in various areas, therefore a new method for finding a solution of the Fredholm fuzzy integral equation is presented. This method converts the fuzzy integral equation into linear system by using the Taylor series. For this scope, first the Taylor expansion of unknown function is substituted in parametric form of the given equation. Then we differentiate...