Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formal...

In this paper we present fuzzy coupled fixed point results in the turf of complete b-metric spaces via nonlinear F-contraction; follow derive some interesting as byproducts. Eventually, apply our solving Volterra integral equations and Caputo-Hadamard type fractional differential equations.

We apply the Radu–Miheţ method derived from an alternative fixed-point theorem with a class of matrix-valued fuzzy controllers to approximate fractional Volterra integro-differential equation ψ-Hilfer derivative in k-normed spaces obtain approximation for this type equation.

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 ...

Abstract: In this paper, a type-2 fuzzy adaptive controller of a Lotak-Volterra system is considered. For bettering the active system properly, the approximated error is introduced into the design of the controller. By using Lyapunov synthesis approach, we attain an adaptive law adjusting the free parameters in the controller such that the closed-loop system follows a desired trajectory. The no...

In this article, we focus on linear and nonlinear fuzzy Volterra integral equations of the second kind and we propose a numerical scheme using homotopy perturbation method (HPM) to obtain fuzzy approximate solutions to them. To facilitate the benefits of this proposal, an algorithmic form of the HPM is also designed to handle the same. In order to illustrate the potentiality of the approach, tw...