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

Yi Tian; Yi Tian

doi:10.3934/mmc.2022009

Mathematical Modelling and Control

2022, Volume 2, Issue 2: 75-80. doi: 10.3934/mmc.2022009

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Research article

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

Yi Tian ^{1,2
,
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1.
College of Data Science and Application, Inner Mongolia University of Technology, Hohhot, China
2.
Inner Mongolia Autonomous Region Engineering and Technology Research Center of Big Data Based Software Service, Hohhot, China

Received: 04 January 2022 Revised: 11 April 2022 Accepted: 03 June 2022 Published: 27 June 2022

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.
- He's fractal derivative,
- semi-inverse method,
- Ying Buzu algorithm,
- Taylor series method,
- variational principle
Citation: Yi Tian. Approximate solution of initial boundary value problems for ordinary differential equations with fractal derivative[J]. Mathematical Modelling and Control, 2022, 2(2): 75-80. doi: 10.3934/mmc.2022009

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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.

References

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