In this study, the implantation of a new semi-analytical method called optimal auxiliary function (OAFM) has been extended to partial differential equations. The adopted was tested upon for approximate solution generalized modified b-equation. first-order numerical obtained by OAFM compared with variational homotopy perturbation (VHPM). possesses and control parameters which can be easily handl...

In this paper, we establish some best proximity point theorems using new proximal contractive mappings in asymmetric $G_{p}$-metric spaces. Our motive is to find an optimal approximate solution of a fixed point equation. We provide best proximity points for cyclic contractive mappings in $G_{p}$-metric spaces. As consequences of these results, we deduce fixed point results in $G_{p}$-metric spa...

In recent years, numerous approaches have been applied for finding the solutions of functional equations. One of them is the optimal homotopy asymptotic method. In current paper, this method has been applied for obtaining the approximate solution of Fisher equation. The reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...

In this paper, He’s variational iteration method (VIM) is used to obtain approximate analytical solutions of the Abelian differential equation. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of problem. The method is capable of reducing the size of calculation...

Friction is a nonlinear phenomenon which has destructive effects on performance of control systems. To obviate these effects, friction compensation is an effectual solution. In this paper, an adaptive technique is proposed in order to eliminate limit cycles as one of the undesired behaviors due to presence of friction in control systems which happen frequently. The proposed approach works for n...

we present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with lr fuzzy variables. as solutions, notions of exact and approximate solutions are considered. we transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. if the corresponding crisp system is incompatible, then the fuzzy ...

Given non-empty subsets A and B of a metric space, let S : A → B and T : A → B be non-self mappings. Taking into account the fact that, given any element x in A, the distance between x and Sx, and the distance between x and Tx are at least d(A,B), a common best proximity point theorem affirms global minimum of both functions x → d(x, Sx) and x → d(x, Tx) by imposing a common approximate solutio...

We consider optimal estimation problems characterized by a state vector with i) dynamics described via a differential equation with Lipschitz nonlinearities, ii) partial information provided via a Lipschitz nonlinear mapping, and iii) an Lp norm measure of the estimation error to be minimized. An approximate solution of such optimal estimation problem is searched for by restricting the optimiza...