Some positive results for exponential-kernel difference operators of Riemann-Liouville type

Pshtiwan Othman Mohammed; Pshtiwan Othman Mohammed

doi:10.3934/mmc.2024012

Mathematical Modelling and Control

2024, Volume 4, Issue 1: 133-140. doi: 10.3934/mmc.2024012

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Research article

Some positive results for exponential-kernel difference operators of Riemann-Liouville type

Pshtiwan Othman Mohammed ^{1,2
,
,}

1.
Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq
2.
Research and Development Center, University of Sulaimani, Sulaymaniyah 46001, Iraq

Received: 18 November 2023 Revised: 05 February 2024 Accepted: 18 February 2024 Published: 08 April 2024

We established positivity of $ \nabla{f} $ obtained from a systematic computation of a composition of sequential fractional differences of the function $ {f} $ that satisfy certain conditions in a negative lower bound setup. First, we considered the different order sequential fractional differences in which we need a complicated condition. Next, we equalled the order of fractional differences and we saw that a simpler condition will be needed. We illustrated our positivity results for an increasing function of the rising type.
- Riemann-Liouville fractional operators,
- exponential kernel,
- positivity analyses,
- negative lower bound
Citation: Pshtiwan Othman Mohammed. Some positive results for exponential-kernel difference operators of Riemann-Liouville type[J]. Mathematical Modelling and Control, 2024, 4(1): 133-140. doi: 10.3934/mmc.2024012

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Abstract

We established positivity of $ \nabla{f} $ obtained from a systematic computation of a composition of sequential fractional differences of the function $ {f} $ that satisfy certain conditions in a negative lower bound setup. First, we considered the different order sequential fractional differences in which we need a complicated condition. Next, we equalled the order of fractional differences and we saw that a simpler condition will be needed. We illustrated our positivity results for an increasing function of the rising type.

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