Functional Equations for Polynomials

Nonlinear functional equations satisfied by orthogonal polynomials

Let c be a linear functional defined by its moments c(x) = ci for i = 0, 1, . . .. We proved that the nonlinear functional equations P (t) = c(P (x)P (x + t)) and P (t) = c(P (x)P (xt)) admit polynomial solutions which are the polynomials belonging to the family of formal orthogonal polynomials with respect to a linear functional related to c. Other types of nonlinear functional equations whose...

Fractional differential equations with Legendre polynomials

Checking Approximate Computations of Polynomials and Functional Equations

Existence and continuous dependence for fractional neutral functional differential equations

In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.

Convergence of an Approach for Solving Fredholm Functional Integral Equations

In this work, we give a product Nyström method for solving a Fredholm functional integral equation (FIE) of the second kind. With this method solving FIE reduce to solving an algebraic system of equations. Then we use some theorems to prove the existence and uniqueness of the system. Finally we investigate the convergence of the method.