Several Types of <i>q</i>-Differential Equations of Higher Order and Properties of Their Solutions

Abstract

The purpose of this paper is to organize various types of higher order q-differential equations that are connected to q-sigmoid polynomials and obtain certain properties regarding their solutions. Using the properties of q-sigmoid polynomials, we show the symmetric properties of q-differential equations of higher order. Moreover, we derive special properties for the approximate roots of q-sigmoid polynomials which are solutions of higher order q-differential equations.

Keywords

• <i>q</i>-derivative
• <i>q</i>-numbers
• <i>q</i>-sigmoid numbers and polynomials
• <i>q</i>-differential equations of higher order
• <i>q</i>-sigmoid polynomials
• symmetric property