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Research Article | Open Access

Approximate solution of initial boundary value problems for ordinary differential equations with fractal derivative

Yi Tian1,2( )
College of Data Science and Application, Inner Mongolia University of Technology, Hohhot, China
Inner Mongolia Autonomous Region Engineering and Technology Research Center of Big Data Based Software Service, Hohhot, China
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Abstract

Fractal ordinary differential equations are successfully established by He's fractal derivative in a fractal space, and their variational principles are obtained by semi-inverse transform method.Taylor series method is used to solve the given fractal equations with initial boundary value conditions, and sometimes Ying Buzu algorithm play an important role in this process. Examples show the Taylor series method and Ying Buzu algorithm are powerful and simple tools.

Keywords

He's fractal derivativesemi-inverse methodYing Buzu algorithmTaylor series methodvariational principle

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Mathematical Modelling and Control
Volume 2 Issue 2,
June 2022
Pages 75-80
DOI: 10.3934/mmc.2022009

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Cite this article:
Tian Y. Approximate solution of initial boundary value problems for ordinary differential equations with fractal derivative. Mathematical Modelling and Control, 2022, 2(2): 75-80. https://doi.org/10.3934/mmc.2022009

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Received: 04 January 2022
Revised: 11 April 2022
Accepted: 03 June 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)