Discrete fractional calculus for interval–valued systems

This study investigates linear fractional difference equations with respect to interval–valued functions. Caputo and Riemann–Liouville differences are defined. w–monotonicity is introduced and discrete Leibniz integral laws are provided. Then exact solutions of two linear equations are obtained by P...

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Bibliographic Details
Published in:Fuzzy sets and systems 2021-02, Vol.404, p.141-158
Main Authors: Huang, Lan-Lan, Wu, Guo-Cheng, Baleanu, Dumitru, Wang, Hong-Yong
Format: Article
Language:English
Subjects:
Discrete fractional calculus
Fractional difference equations
Interval–valued functions
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Summary:This study investigates linear fractional difference equations with respect to interval–valued functions. Caputo and Riemann–Liouville differences are defined. w–monotonicity is introduced and discrete Leibniz integral laws are provided. Then exact solutions of two linear equations are obtained by Picard's iteration. In comparison with the deterministic initial problems, the solutions are given in discrete Mittag–Leffler functions with and without delay, respectively. This paper provides a novel tool to understand fractional uncertainty problems on discrete time domains.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2020.04.008