In this paper, we introduce hybrid of block-pulse functions and Bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. Then, we utilize them to solve delay differential equations and time-delay system. The method is based upon e...

This work overviews the single-particle two-way communication protocol recently introduced by del Santo and Dakić (dSD), analyses it using process matrix formalism. We give a detailed account of importance operational meaning interaction an agent with vacuum – in particular its role description. Our analysis shows that should be treated as operation, on equal footing all other interactions. rai...

The problems of systems identification, analysis and optimal control have been recently studied using orthogonal functions. The specific orthogonal functions used up to now are the Walsh, the block-pulse, the Laguerre, the Legendre, Haar and many other functions. In the present paper, several operational matrices for integration and differentiation are studied. we introduce the Kronecker convol...

and Applied Analysis 3 The vector representation of the above-mentioned truncated series can be written in the following form: y N (t)

In this paper, we propose and analyze an efficient matrix method based on Bell polynomials for numerically solving nonlinear Fredholm- Volterra integral equations. For this aim, first we calculate operational matrix of integration and product based on Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the system of nonlinear algebraic equations w...