The introduced method in this study consists of reducing a system of infinite boundary integro-differential equations (IBI-DE) into a system of al- gebraic equations, by expanding the unknown functions, as a series in terms of Laguerre polynomials with unknown coefficients. Properties of these polynomials and operational matrix of integration are rst presented. Finally, two examples illustra...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

This paper considers the computation of greatest common divisor (GCD) dt1,t2(x,y) three bivariate Bernstein polynomials that are defined in a rectangular domain, where t1(t2) is degree when it written as polynomial x(y) whose coefficients y(x). The Sylvester resultant matrix and its subresultant matrices used for degrees GCD. It shown there four forms these they differ their computational prope...

We introduce common generalization of (double) Schubert, Grothendieck, Demazure, dual and stable Grothendieck polynomials, and Di Francesco–Zinn-Justin polynomials. Our approach is based on the study of algebraic and combinatorial properties of the reduced rectangular plactic algebra and associated Cauchy kernels.

The aim of this paper is to define and study of the Gegenbauer matrix polynomials of two variables. An explicit representation, a three-term matrix recurrence relations, differential recurrence relations and hypergeometric matrix representation for the Gegenbauer matrix polynomials of two variables are given. The Gegenbauer matrix polynomials are solutions of the matrix differential equations a...

The finite Pfaff lattice is given by commuting Lax pairs involving a finite matrix L (zero above the first subdiagonal) and a projection onto Sp(N). The lattice admits solutions such that the entries of the matrix L are rational in the time parameters t1, t2, . . . , after conjugation by a diagonal matrix. The sequence of polynomial τ -functions, solving the problem, belongs to an intriguing ch...