An Improved Precise Integration Method for Fractional Ordinary Differential Equations

BAO Siyuan; SHEN Feng

doi:10.21656/1000-0887.390355

Volume 40 Issue 12

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BAO Siyuan, SHEN Feng. An Improved Precise Integration Method for Fractional Ordinary Differential Equations[J]. Applied Mathematics and Mechanics, 2019, 40(12): 1309-1320. doi: 10.21656/1000-0887.390355

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An Improved Precise Integration Method for Fractional Ordinary Differential Equations

doi: 10.21656/1000-0887.390355

BAO Siyuan^1,2,
SHEN Feng²

¹Key Laboratory of Structural Engineering of Jiangsu Province,Suzhou University of Science and Technology, Suzhou, Jiangsu 215011,P.R.China;²Department of Engineering Mechanics, School of Civil Engineering,Suzhou University of Science and Technology, Suzhou, Jiangsu 215011, P.R.China

Funds: The National Natural Science Foundation of China(11202146；51709194)

Received Date: 2018-12-24
Rev Recd Date: 2019-04-09
Publish Date: 2019-12-01

Abstract

Abstract

Based on the definition of the Mittag-Leffler function, the precise iteration computation scheme for the Mittag-Leffler matrix function was constructed. Compared with the normal iteration scheme for exponential functions, the constructed scheme has additional correction items. The expression of the correction item is related to the order of the fractional derivative. For dynamic fractional ordinary differential equation D^(α)v=Hv with the Caputo fractional definition, the solution function value at the endpoint of the time phase can be obtained with the precise iteration method. The numerical examples demonstrated effectiveness and efficiency of the presented method.
- Mittag-Leffler function,
- precise iteration scheme,
- correction item,
- ordinary fractional differential equation,
- Caputo derivative

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References

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