Properties of q-Differential Equations of Higher Order and Visualization of Fractal Using q-Bernoulli Polynomials

Fractal and Fractional

Jung-Yoog Kang¹  Cheon-Seoung Ryoo² 

[1] Department of Mathematics Education, Silla University, Busan 46958, Korea;Department of Mathematics, Hannam University, Daejeon 34430, Korea;

关键词: q-Bernoulli polynomials;    q-difference equation of higher order;    Mandelbrot set;    Julia set;   

DOI  :  10.3390/fractalfract6060296

来源: DOAJ

【 摘 要 】

We introduce several q-differential equations of higher order which are related to q-Bernoulli polynomials and obtain a symmetric property of q-differential equations of higher order in this paper. By giving q-varying variations, we identify the shape of the approximate roots of q-Bernoulli polynomials, a solution of q-differential equations of higher order, and find several conjectures associated with them. Furthermore, based on q-Bernoulli polynomials, we create a Mandelbrot set and a Julia set to find a variety of related figures.

【 授权许可】

Unknown