A TUTORIAL INTRODUCTION TO THE TWO-SCALE FRACTAL CALCULUS AND ITS APPLICATION TO THE FRACTAL ZHIBER–SHABAT OSCILLATOR

Author:

HE JI-HUAN123,EL-DIB YUSRY O.4

Affiliation:

1. School of Science, School of Science, Xi’an University of Architecture and Technology, Xi’an, P. R. China

2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China

3. National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-Ai Road, Suzhou, P. R. China

4. Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

Abstract

In this paper, a tutorial introduction to the two-scale fractal calculus is given. The two-scale fractal derivative is conformable with the traditional differential derivatives. When the fractal dimensions tend to an integer value, its basic properties are discussed, and the fractal Zhiber–Shabat oscillator is used as an example to reveal the basic properties of a fractal differential equation. The two-scale transform is used to convert the nonlinear Zhiber–Shabat oscillator with the fractal derivatives to the traditional model. The homotopy perturbation method has been demonstrated under a suitable transformation of the system containing several exponential nonlinear terms to the famous Helmholtz–Duffing oscillator. Stability behavior is discussed. Several numerical illustrations are also provided to exhibit the integrity of the introduced formulation. It is demonstrated that the proposed formulation is accurate enough for highly nonlinear differential equations containing large nonlinear terms.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Cited by 67 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3