In this paper we propose a new approach to fuzzy stochastic integrals of Itô and Aumann type. Then a fuzzy equation with fuzzy stochastic integrals is investigated. The existence and uniqueness of solution is proven. Some typical properties of the solution are also obtained. Similar results to set-valued stochastic integral equations are stated.

New existence results are presented for fuzzy differential and integral equations. Our analysis combines the stacking theorem with results concerning the maximal solution for an appropriate differential equation.

Abstract The purpose of this manuscript is to obtain some fixed point results in generalized controlled fuzzy metric spaces. Our generalize and extend many the previous findings same approach. Moreover, two examples support our theorems are obtained. Finally, examine strengthen theoretical results, existence uniqueness solution a nonlinear integral equation studied as kind application.

In this paper, a new approach to determine the numerical solution of two-dimensional fuzzy Fredholm integral equation of the second kind (2DFFIE2) is proposed. This method is based on the fuzzy bivariate Bernstein polynomials. By using fuzzy bivariate Bernstein polynomials, a 2DFFIE2 can be transformed to a dual fuzzy linear system. The error estimate of this method is presented in terms of the...

In this paper we introduce the notion of fuzzy Hilbert spaces and deduce the fuzzy version of Riesz representation theorem. Also we prove some results in fixed point theory and utilize the results to study the existence and uniqueness of solution of Uryson’s integral equation.

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 this paper, the existence and uniqueness of the solution of a nonlinear fully fuzzy implicit integro-differential equation arising in the field of fluid mechanics is investigated. First, an equivalency lemma is presented by which the problem understudy is converted to the two different forms of integral equation depending on the kind of differentiability of the solution. Then, the conditions...

This paper discusses about the solution of fuzzy Volterra integral equation of first-kind (F-VIE1) using spectral method. The parametric form of fuzzy driving term is applied for F-VIE1, then three classifications for (F-VIE1) are searched to solve them. These classifications are considered based on the interval sign of the kernel. The Gauss-Legendre points and Legendre weights for arithmetics ...