In this paper, operational matrix method based upon the Bernstein polynomials is proposed to solve the variable order fractional integro-differential equations in the Caputo derivative sense. We derive the Bernstein polynomials operational matrix of fractional order integration and introduce the product operational matrix of Bernstein polynomials. A truncated the Bernstein polynomials series to...

A binary matrix can be scanned by moving a fixed rectangular window (submatrix) across it, rather like examining it closely under a microscope. With each viewing, a convenient measurement is the number of 1s visible in the window, which might be thought of as the luminosity of the window. The rectangular scan of the binary matrix is then the collection of these luminosities presented in matrix ...

In this paper‎, ‎first‎, ‎a numerical method is presented for solving a class of linear Fredholm integro-differential equation‎. ‎The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions‎. ‎The application of the proposed operational matrix with tau method is then utilized to transform the integro-differential equations to...

In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied.  Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of ...