A NEW PERSPECTIVE TO STUDY THE THIRD-ORDER MODIFIED KDV EQUATION ON FRACTAL SET-Reference-Cited by-同舟云学术

A NEW PERSPECTIVE TO STUDY THE THIRD-ORDER MODIFIED KDV EQUATION ON FRACTAL SET

Published:2020-09 Issue:06 Volume:28 Page:2050110
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

LIU JIAN-GEN¹²^ORCID,YANG XIAO-JUN¹²³,FENG YI-YING²³,CUI PING²⁴

Affiliation:

1. School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China

2. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China

3. School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China

4. School of Mathematics and Statistics, Qujing Normal University, Qujing, Yunnan 655000, P. R. China

Abstract

In this paper, we construct the Bäcklund transformations and the super-position formulas to the constant coefficients local fractional Riccati equation for the first time. Next, by means of the Bäcklund transformations and seed solutions which have been known in [X. J. Yang et al., Non-differentiable solutions for local fractional nonlinear Riccati differential equations, Fundam. Inform. 151(1–4) (2017) 409–417], we can get a class of exact solutions to the third-order modified KdV equation on the fractal set. These new type solutions can assist us to review different nonlinear phenomena better, which had been modeled via local fractional derivative.

Funder

Yue-Qi Scholar of the China University of Mining and Technology

333 Project of Jiangsu Province

Joint Special Fund for Fundamental Research of Local Undergraduate Universities(Partial) in Yunnan Province

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X20501108

Reference20 articles.

1. Auxiliary equation method for time-fractional differential equations with conformable derivative