By using a random version of the theory of contractor introduced by Altman, we introduce and study a system of nonlinear operator equations for a mixed family of fuzzy and crisp operators in probabilistic normed spaces. We construct some new iterative algorithms for solving this kind of nonlinear operator equations. We also prove some new existence theorems of solutions of a new system of nonli...

In this paper, we introduce an approach by using inverse fuzzy transforms based on the fuzzy partition with combination in collocation technique for the numerical solution of Fredholm integral equations of the second kind. The main advantage of this approach is to reduce the problem to the linear system of equations. We present the convergence theorem for this method. Finally, we give two examp...

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...

The bending of a rectangular elastic plate under uniform distributed load and simply supported at the corners by equal-leg angles is studied analytically. The width of the supporting legs can be varied symmetrically about the plate axes giving mixed boundary conditions with supported and free edges. The solution is set up by using the Le'vy-Na'dai approach and the mixed boundary equation at the...

controller design remains an elusive and challenging problem foruncertain nonlinear dynamics. interval type-2 fuzzy logic systems (it2fls) incomparison with type-1 fuzzy logic systems claim to effectively handle systemuncertainties especially in the presence of disturbances and noises, but lack aformal mechanism to guarantee performance. in contrast, adaptive sliding modecontrol (asmc) provides...

in this paper, we apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...

The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for s...

In this paper‎, ‎existence of an $L^p$-solution for 2DIEs (Two‎ ‎Dimensional Integral Equations) of the Hammerstein type is‎ ‎discussed‎. ‎The main tools in this discussion are Schaefer's and‎ ‎Schauder's fixed point theorems with a general version of‎ ‎Gronwall's inequality‎.