On analysing discrete sequential operators of fractional order and their monotonicity results

Pshtiwan Othman Mohammed; Musawa Yahya Almusawa; Pshtiwan Othman Mohammed; Musawa Yahya Almusawa

doi:10.3934/math.2023649

AIMS Mathematics

2023, Volume 8, Issue 6: 12872-12888. doi: 10.3934/math.2023649

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Research article

On analysing discrete sequential operators of fractional order and their monotonicity results

Pshtiwan Othman Mohammed ^{1
,
,},
Musawa Yahya Almusawa ^{2
,
,}

1.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
2.
Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia

Received: 14 February 2023 Revised: 18 March 2023 Accepted: 28 March 2023 Published: 31 March 2023
MSC : 39A12, 39B62, 33B10, 26A48, 26A51

In this study, we consider the analysis of monotonicity for the Riemann-Liouville fractional differences of sequential type. The results are defined on the subsets of $ (0, 1)\times(0, 1) $ with a certain restriction. By analysing the difference operator in the point-wise form into a delta form, we use the standard sequential formulas as stated in Theorems 2.1 and 2.2 to establish the positivity of the delta difference operator of the proposed the discrete sequential operators. Finally, some numerical experiments are conducted which confirm our theoretical monotonicity results.
- delta Riemann-Liouville fractional difference,
- sequential operators,
- monotonicity analysis
Citation: Pshtiwan Othman Mohammed, Musawa Yahya Almusawa. On analysing discrete sequential operators of fractional order and their monotonicity results[J]. AIMS Mathematics, 2023, 8(6): 12872-12888. doi: 10.3934/math.2023649

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Abstract

In this study, we consider the analysis of monotonicity for the Riemann-Liouville fractional differences of sequential type. The results are defined on the subsets of $ (0, 1)\times(0, 1) $ with a certain restriction. By analysing the difference operator in the point-wise form into a delta form, we use the standard sequential formulas as stated in Theorems 2.1 and 2.2 to establish the positivity of the delta difference operator of the proposed the discrete sequential operators. Finally, some numerical experiments are conducted which confirm our theoretical monotonicity results.

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