Analysis reveals that nonlocal discrete operators exhibit a pathological property in sequences, indicating unique behavior.
We demonstrate that there exist sequences { u n } n = 0 ∞ ⊆ ( 0 , + ∞ ) \{ uₙ \}n = 0∞ ⊆ (0, +∞ ) such that u n + 1 > u n un + 1> uₙ for each n ∈ N 0 n∈ N₀ , but yet the fractional difference of the sequence is uniformly negative. This demonstrates a pathological property of nonlocal discrete operators.
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Chang et al. (2026) studied this question.
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