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Positivity and monotonicity results for triple sequential fractional differences via convolution

  • Christopher S. Goodrich ORCID logo EMAIL logo and Benjamin Lyons
From the journal Analysis

Abstract

We investigate the relationship between the discrete fractional difference

(ΔγΔβΔαf)(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., (ΔβΔαf)(t), there is relatively more complexity observed.

Acknowledgements

The authors would like to thank the anonymous referee for his or her very helpful comments regarding the original manuscript.

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Received: 2019-10-11
Revised: 2020-02-24
Accepted: 2020-02-28
Published Online: 2020-04-25
Published in Print: 2020-05-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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