On the Solution of Fractional Differential-Algebraic Systems With the Adomian Decomposition Method

FENG Zai-yong; CHEN Ning

doi:10.3879/j.issn.1000-0887.2015.11.009

Volume 36 Issue 11

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FENG Zai-yong, CHEN Ning. On the Solution of Fractional Differential-Algebraic Systems With the Adomian Decomposition Method[J]. Applied Mathematics and Mechanics, 2015, 36(11): 1211-1218. doi: 10.3879/j.issn.1000-0887.2015.11.009

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On the Solution of Fractional Differential-Algebraic Systems With the Adomian Decomposition Method

doi: 10.3879/j.issn.1000-0887.2015.11.009

FENG Zai-yong^1,2,
CHEN Ning¹

¹College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, P.R.China;²Department of Social Science, Nanjing Institute of Railway Technology, Nanjing 210031, P.R.China

Funds: The National Natural Science Foundation of China(11272159)

Received Date: 2015-05-14
Rev Recd Date: 2015-07-17
Publish Date: 2015-11-15

Abstract

Abstract

The solution of the fractional differentialalgebraic systems (FDASs) was studied with the Adomian decomposition method. The influence of the algebraic constraints on the Adomian decomposition method was investigated, and the main difficulty of transforming the FDASs into fractional differential systems through solving the algebraic constraints directly was pointed out. To determine the components of the algebraic variable series solution, a new method was presented with the Adomian decomposition implemented successfully to obtain the solution of the FDAS. The solution of the FDAS under linear algebraic constraints was particularly discussed with the Adomian decomposition method. It’s proved that the linear relationship between the variables under algebraic constraints could be equivalently transformed into the linear relationship between the components of the corresponding series solution. 2 examples were given to illustrate the convenience and effectiveness of the proposed method.
- fractional order,
- differential-algebraic system,
- Adomian decomposition,
- series solution,
- linear constraint

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References(16)

References

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