Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 69, Issue -, Pages 198-218Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2018.09.024
Keywords
Discrete fractional calculus; Short memory principle; Long memory characteristic; Series representation
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Funding
- National Natural Science Foundation of China [61601431, 61573332]
- Anhui Provincial Natural Science Foundation [1708085QF141]
- Alexander von Humboldt Foundation of Germany
- Fundamental Research Funds for the Central Universities [WK2100100028]
- China Postdoctoral Science Foundation [2016M602032]
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This paper addresses the description and analysis problems of nabla discrete fractional calculus. The series representation framework is developed first, including two Taylor series expanded at the initial instant and the current time, respectively. Under this framework, several essential properties of fractional sum/difference are presented and investigated. Notably, the short memory principle is introduced for nabla discrete fractional calculus, along with which two corresponding series are studied. (C) 2018 Elsevier B.V. All rights reserved.
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