1. Fractional discrete-time diffusion equation with uncertainty: Applications of fuzzy discrete fractional calculus.
- Author
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Huang, Lan-Lan, Baleanu, Dumitru, Mo, Zhi-Wen, and Wu, Guo-Cheng
- Subjects
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FRACTIONAL calculus , *DISCRETE choice models , *DECISION making , *DISCRETE geometry , *FRACTIONAL differential equations - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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