Solving Some Physics Problems Involving Fractional-Order Differential Equations with the Morgan-Voyce Polynomials

Solving the fractional integro-differential equations using fractional order Jacobi polynomials

In this paper, we are intend to present a numerical algorithm for computing approximate solution of linear and nonlinear Fredholm, Volterra and Fredholm-Volterra  integro-differential equations. The approximated solution is written in terms of fractional Jacobi polynomials. In this way, firstly we define Riemann-Liouville fractional operational matrix of fractional order Jacobi polynomials, the...

Fractional differential equations with Legendre polynomials

Some relations between Kekule structure and Morgan-Voyce polynomials

In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) Morgan-Voyce polynomial equal to the number of k-matchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zig-zag nonbranched catacondensed benzenid chains and Morgan-Voyce polynomials and between regularly zig-zag ...

A spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations

In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...

Generalizations of Modified Morgan-voyce Polynomials

In two recent articles [2] and [3], Ferri et al. introduced and studied the properties of two numerical triangles, which they called DFF and DFZ triangles. However, in a subsequent article, Andre-Jeannin [1] showed that the polynomials generated by the rows of these triangles are indeed the Morgan-Voyce polynomials Bn{x) and bn(x), whose properties are well known [10] and [11]; in fact, the pol...