Fractional discrete-time diffusion equation with uncertainty: Applications of fuzzy discrete fractional calculus

Lan-Lan Huang, Dumitru Baleanu, Zhi-Wen Mo and Guo-Cheng Wu

Physica A: Statistical Mechanics and its Applications, 2018, vol. 508, issue C, 166-175

Abstract: This study provides some basics of fuzzy discrete fractional calculus as well as applications to fuzzy fractional discrete-time equations. With theories of r-cut set, fuzzy Caputo and Riemann–Liouville fractional differences are defined on a isolated time scale. Discrete Leibniz integral law is given by use of w-monotonicity conditions. Furthermore, equivalent fractional sum equations are established. Fuzzy discrete Mittag-Leffler functions are obtained by the Picard approximation. Finally, fractional discrete-time diffusion equations with uncertainty is investigated and exact solutions are expressed in form of two kinds of fuzzy discrete Mittag-Leffler functions. This paper suggests a discrete time tool for modeling discrete fractional systems with uncertainty.

Keywords: Fractional difference equations; Fuzzy-valued functions; Time scale (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:508:y:2018:i:c:p:166-175

DOI: 10.1016/j.physa.2018.03.092

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