This paper presents a semianalytical method, the modified multistep differential transform method (MMSDTM), for solving linear and nonlinear fractional-order differential equations with the order between 0 and 2. This method can be considered as a variant of the predictor-corrector method (PCM). The multistep differential transform method (MSDTM), which does not take the memory effect into account and yields unsatisfactory solution very rapidly, is first used to find an estimation as the predictor of the solution. In the corrector procedure, the memory term associated with the fractional-order derivative is decomposed by the subtraction of two integrals; one is abnormal with singularity and the other is normal without singularity and the two integrals are calculated by using the MSDTM and a simple numerical scheme, respectively. Four illustrative examples are given to show that the MMSDTM requires much less computational cost and retains high computational accuracy, compared with the widely used PCM.
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January 2013
Research-Article
A Modified Multi-Step Differential Transform Method for Solving Fractional Dynamic Systems
Zaihua Wang,
Zaihua Wang
1
e-mail: zhwang@nuaa.edu.cn
State Key Laboratory of Mechanics and Control of Mechanical Structures,
State Key Laboratory of Mechanics and Control of Mechanical Structures,
Nanjing University of Aeronautics and Astronautics
,210016 Nanjing
, China
1Corresponding author.
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Maolin Du
Maolin Du
Institute of Science,
e-mail: dumaolindml@yahoo.com.cn
PLA University of Science and Technology
,211101 Nanjing
, China
e-mail: dumaolindml@yahoo.com.cn
Search for other works by this author on:
Min Shi
e-mail: 15996301586@163.com
Zaihua Wang
e-mail: zhwang@nuaa.edu.cn
State Key Laboratory of Mechanics and Control of Mechanical Structures,
State Key Laboratory of Mechanics and Control of Mechanical Structures,
Nanjing University of Aeronautics and Astronautics
,210016 Nanjing
, China
Maolin Du
Institute of Science,
e-mail: dumaolindml@yahoo.com.cn
PLA University of Science and Technology
,211101 Nanjing
, China
e-mail: dumaolindml@yahoo.com.cn
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 23, 2011; final manuscript received March 28, 2012; published online June 14, 2012. Assoc. Editor: J. A. Tenreiro Machado.
J. Comput. Nonlinear Dynam. Jan 2013, 8(1): 011008 (8 pages)
Published Online: June 14, 2012
Article history
Received:
October 23, 2011
Revision Received:
March 28, 2012
Citation
Shi, M., Wang, Z., and Du, M. (June 14, 2012). "A Modified Multi-Step Differential Transform Method for Solving Fractional Dynamic Systems." ASME. J. Comput. Nonlinear Dynam. January 2013; 8(1): 011008. https://doi.org/10.1115/1.4006572
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