NON-DIFFERENTIABLE EXACT SOLUTIONS FOR THE NONLINEAR ODES DEFINED ON FRACTAL SETS-Reference-Cited by-同舟云学术

NON-DIFFERENTIABLE EXACT SOLUTIONS FOR THE NONLINEAR ODES DEFINED ON FRACTAL SETS

Published:2017-07-25 Issue:04 Volume:25 Page:1740002
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

YANG XIAO-JUN¹,GAO FENG¹,SRIVASTAVA H. M.²³

Affiliation:

1. State Key Laboratory for Geo-Mechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China

2. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada

3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China

Abstract

In the present paper, a family of the special functions via the celebrated Mittag–Leffler function defined on the Cantor sets is investigated. The nonlinear local fractional ODEs (NLFODEs) are presented by following the rules of local fractional derivative (LFD). The exact solutions for these problems are also discussed with the aid of the non-differentiable charts on Cantor sets. The obtained results are important for describing the characteristics of the fractal special functions.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X17400023

Reference44 articles.

1. Fractional Calculus and Waves in Linear Viscoelasticity

2. Fractional Calculus: Quo Vadimus? (Where are we Going?)

3. On Mittag-Leffler-type functions in fractional evolution processes

4. Mittag–Leffler stability of fractional order nonlinear dynamic systems

Cited by 73 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

1. Darboux and generalized Darboux transformations for the fractional integrable derivative nonlinear Schrödinger equation;International Journal of Geometric Methods in Modern Physics;2024-06-29

2. A NOVEL COMPUTATIONAL APPROACH TO THE LOCAL FRACTIONAL (3+1)-DIMENSIONAL MODIFIED ZAKHAROV–KUZNETSOV EQUATION;Fractals;2024-01

3. STUDY ON THE LOCAL FRACTIONAL (3+1)-DIMENSIONAL MODIFIED ZAKHAROV–KUZNETSOV EQUATION BY A SIMPLE APPROACH;Fractals;2024-01

4. Dynamic behaviors of the non-linear local fractional heat conduction equation on the cantor sets;Thermal Science;2024

5. New exact solutions of the local fractional (3+1)-dimensional Kadomstev-Petviashvili equation;Thermal Science;2024