Huang, Lan-LanBaleanu, DumitruBaleanu, DumitruMo, Zhi-WenWu, Guo-Cheng2020-03-242020-03-242018Huang, Lan-Lan...et al. (2018). "Fractional discrete-time diffusion equation with uncertainty: Applications of fuzzy discrete fractional calculus", Physica a-Statistical Mechanics and its Applications, Vol. 508, pp. 166-175.0378-43711873-2119https://doi.org/10.1016/j.physa.2018.03.092Huang, Lan-Lan/0000-0002-6375-9183; Wu, Guo-Cheng/0000-0002-1946-6770This 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. (C) 2018 Elsevier B.V. All rights reserved.eninfo:eu-repo/semantics/closedAccessFractional Difference EquationsFuzzy-Valued FunctionsTime ScaleArticle50816617510.1016/j.physa.2018.03.0922-s2.0-85047615666WOS:000440122200017N/AQ1