Analytical and Numerical Monotonicity Analyses for Discrete Delta Fractional Operators
Abstract
:1. Introduction
- We consider the delta fractional difference together with two conditions as stated in Theorem 1, to get one time step positivity .
- We introduce a set as defined in (5) and then we show that this set is decreasing for each values and .
- The decreasing of this set makes the first theorem (Theorem 1) to be correct for each value of t in . This result will be proved in Corollary 1.
- Finally, the possibility of the negative lower bound will be demonstrated by numerical simulation of the sets .
2. Basic Definitions
3. Negative Lower Bound Results
4. Numerical Performances
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Nonlaopon, K.; Mohammed, P.O.; Hamed, Y.S.; Muhammad, R.S.; Brzo, A.B.; Aydi, H. Analytical and Numerical Monotonicity Analyses for Discrete Delta Fractional Operators. Mathematics 2022, 10, 1753. https://doi.org/10.3390/math10101753
Nonlaopon K, Mohammed PO, Hamed YS, Muhammad RS, Brzo AB, Aydi H. Analytical and Numerical Monotonicity Analyses for Discrete Delta Fractional Operators. Mathematics. 2022; 10(10):1753. https://doi.org/10.3390/math10101753
Chicago/Turabian StyleNonlaopon, Kamsing, Pshtiwan Othman Mohammed, Y. S. Hamed, Rebwar Salih Muhammad, Aram Bahroz Brzo, and Hassen Aydi. 2022. "Analytical and Numerical Monotonicity Analyses for Discrete Delta Fractional Operators" Mathematics 10, no. 10: 1753. https://doi.org/10.3390/math10101753