Positivity and monotonicity results for triple sequential fractional differences via convolution

Abstract

Abstract We investigate the relationship between the discrete fractional difference (\Delta^{\gamma}\circ\Delta^{\beta}\circ\Delta^{\alpha}f)(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., {(\Delta^{\beta}\circ\Delta^{\alpha}f)(t)} , there is relatively more complexity observed.

Topics & Concepts