Various Types of <i>q</i>-Differential Equations of Higher Order for <i>q</i>-Euler and <i>q</i>-Genocchi Polynomials

Abstract

One finds several q-differential equations of a higher order for q-Euler polynomials and q-Genocchi polynomials. Additionally, we have a few q-differential equations of a higher order, which are mixed with q-Euler numbers and q-Genocchi polynomials. Moreover, we investigate some symmetric q-differential equations of a higher order by applying symmetric properties of q-Euler polynomials and q-Genocchi polynomials.

Keywords

• <i>q</i>-Euler polynomials
• <i>q</i>-Genocchi polynomials
• <i>q</i>-differential equation of higher order
• symmetric property