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EXACT TRAVELING-WAVE SOLUTION FOR LOCAL FRACTIONAL BOUSSINESQ EQUATION IN FRACTAL DOMAIN

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

E-mail Address: dyangxiaojun@163.com

Corresponding author.

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J. A. TENREIRO MACHADO

Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. António Bernardino de Almeida, 4249-015 Porto, Portugal

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, and

DUMITRU BALEANU

Department of Mathematics, Cankya University, Ogretmenler Cad. 14, Balgat-06530, Ankara, Turkey

Institute of Space Sciences, Magurele-Bucharest, Romania

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https://doi.org/10.1142/S0218348X17400060Cited by:167 (Source: Crossref)

This article is part of the issue:

Special Issue on Advanced Fractal Computing Theorem and Application

Abstract

The new Boussinesq-type model in a fractal domain is derived based on the formulation of the local fractional derivative. The novel traveling wave transform of the non-differentiable type is adopted to convert the local fractional Boussinesq equation into a nonlinear local fractional ODE. The exact traveling wave solution is also obtained with aid of the non-differentiable graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains.

Keywords:

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History

Received 23 February 2017

Revised 29 March 2017

Accepted 6 April 2017

Published: June 2, 2017

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This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.

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EXACT TRAVELING-WAVE SOLUTION FOR LOCAL FRACTIONAL BOUSSINESQ EQUATION IN FRACTAL DOMAIN

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