let a; b; k 2 k and u ; v 2 u(k). we show for any idempotent e 2 k, ( a 0 b 0 ) is e-clean i ( a 0 u(vb + ka) 0 ) is e-clean and if ( a 0 b 0 ) is 0-clean, ( ua 0 u(vb + ka) 0 ) is too.

Chebyshev Wavelets of the third kind are proposed in this study to solve nonlinear systems FDEs. The main goal method is convert FDE into a system algebraic equations that can be easily solved using matrix methods. In order achieve this, we first generate operational matrices for fractional integration and block-pulse functions (BPF) function approximation. Since obtained sparse, numerical fast...

Alternative Legendre polynomials (ALPs) are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given an...

In this paper, Semi-orthogonal (SO) B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of linear and non-linear second order Fredholm integro-differential equations. The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this functions are presented to reduce the solution of linear and...

A numerical method for finding the solution of nonlinear VolterraHammerstein integral equations is proposed. The properties of the hybrid functions which consists of block-pulse functions plus rationalized Haar functions are presented. The hybrid functions together with the operational matrices of integration and product are then utilized to reduce the solution of nonlinear Volterra-Hammerstein...

In this paper an iterative method based on shifted Legendre polynomials is presented to obtain the approximate solutions of optimal control problems subject to integral equations. The operational matrices of integration and product of shifted Legendre polynomials for solving integral equation is employed. The methodology is based on the parametrization of control and state functions. This conve...

In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative exampl...

To fully quantify the impact of the homecare and hospice industry within the various geographical areas throughout this study, Tripp Umbach established a comprehensive, yet conservative, methodology to estimate the operational impact based on information compiled using uniform and consistent techniques that could be replicated in the future. Using IMPLAN (IMpact analysis for PLANning) data and ...

Abstract. The main purpose of this article is to present an approximate solution for the one dimensional wave equation subject to an integral conservation condition in terms of second kind Chebyshev polynomials. The operational matrices of integration and derivation are introduced and utilized to reduce the wave equation and the conditions into the matrix equations which correspond to a system ...

In this paper, a numerical method for solving LNFODE (Linear Non-homogenous Fractional Ordinary Differential Equation) is presented. The method presented is based on Bernstein polynomials approximation. The operational matrices of integration, differentiation and products are introduced and utilized to reduce the LNFODE problem in order to solve algebraic equations. The method is general, easy ...