Positivity and monotonicity results for triple sequential fractional differences via convolution

We investigate the relationship between the discrete fractional difference (Δγ∘Δβ∘Δαf)(t) and the positivity or monotonicity of the function f . Our approach relies on interpreting the fractional difference as an appropriate convolution operator. The results we provide demonstrate that when compared to the double sequential case, i.e., {(Δβ∘Δαf)(t)} , there is relatively more complexity observed.