Two monotonicity results for nabla and delta fractional differences. (English) Zbl 1327.39011

The authors establish two monotonicity results for the nabla and delta fractional differences (Theorems A and B), which emphasize a nontrivial differences between these two concepts. Moreover, Theorem B implies that Corollary 2.3 in the paper by R. Dahal and Ch. S. Goodrich [Arch. Math. 102, No. 3, 293–299 (2014; Zbl 1296.39016)] is incorrect without an additional assumption, cf. the erratum of R. Dahal and Ch. S. Goodrich [ibid. 104, No. 6, Article ID 771, 599–600 (2015; Zbl 1330.39022)]. This fact is also illustrated by a counterexample.


39A70 Difference operators
39A12 Discrete version of topics in analysis
26A33 Fractional derivatives and integrals
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