A General Differential Equation for Classical Polynomials

Brenstien polynomials and its application to fractional differential equation

The paper is devoted to the study of Brenstien Polynomials and development of some new operational matrices of fractional order integrations and derivatives. The operational matrices are used to convert fractional order differential equations to systems of algebraic equations. A simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is ...

Classical 2-orthogonal polynomials and differential equations

We construct the linear differential equations of third order satisfied by the classical 2orthogonal polynomials. We show that these differential equations have the following form: R4,n(x)P (3) n+3(x)+R3,n(x)P ′′ n+3(x)+R2,n(x)P ′ n+3(x)+R1,n(x)Pn+3(x)=0, where the coefficients {Rk,n(x)}k=1,4 are polynomials whose degrees are, respectively, less than or equal to 4, 3, 2, and 1. We also show tha...

A General Dynamic Function for the Basal Area of Individual Trees Derived from a Production Theoretically Motivated Autonomous Differential Equation

The management of forests may be motivated from production economic and environmental perspectives. The dynamically changing properties of trees affect environmental objectives and values of trees as raw material in the construction sector and in the energy sector. In order to optimize the management of forests, it is necessary to have access to reliable functions that predict how trees develop...

A method for solving first order fuzzy differential equation

Self-adjoint differential equations for classical orthogonal polynomials

This paper deals with spectral type differential equations of the self-adjoint differential operator, 2r order: L(2r)[Y ](x)= 1 (x) d dxr ( (x) r (x) dY (x) dxr ) = rnY (x). If (x) is the weight function and (x) is a second degree polynomial function, then the corresponding classical orthogonal polynomials, {Qn(x)}∞n=0, are shown to satisfy this differential equation when rn is given by rn = r−...