A Study of Monotonicity Analysis for the Delta and Nabla Discrete Fractional Operators of the Liouville

A Study of Monotonicity Analysis for the Delta and Nabla Discrete Fractional Operators of the Liouville–Caputo Family

Published:2023-01-22 Issue:2 Volume:12 Page:114
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Mohammed Pshtiwan Othman¹^ORCID,Goodrich Christopher S.²^ORCID,Srivastava Hari Mohan³⁴⁵⁶^ORCID,Al-Sarairah Eman⁷⁸^ORCID,Hamed Y. S.⁹^ORCID

Affiliation:

1. Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq

2. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

3. Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada

4. Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan

5. Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea

6. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

7. Department of Mathematics, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates

8. Department of Mathematics, Al-Hussein Bin Talal University, P.O. Box 33011, Ma’an 71111, Jordan

9. Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Abstract

In the present article, we explore the correlation between the sign of a Liouville–Caputo-type difference operator and the monotone behavior of the function upon which the difference operator acts. Finally, an example is also provided to demonstrate the application and the validation of the results which we have proved herein.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/2/114/pdf

Reference42 articles.

1. A transform method in discrete fractional calculus;Atici;Int. J. Differ. Equ.,2007

2. Discrete fractional calculus with the nabla operator;Atici;Electron. J. Qual. Theory Differ. Equ.,2009

3. Initial value problems in discrete fractional calculus;Atici;Proc. Am. Math. Soc.,2009

4. Arbitrary order fractional difference operators with discrete exponential kernels and applications;Abdeljawad;Discrete Dyn. Nat. Soc.,2017

5. On the definitions of nabla fractional operators;Abdeljawad;Abstr. Appl. Anal.,2012

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Theoretical Investigation of Fractional Estimations in Liouville–Caputo Operators of Mixed Order with Applications;Axioms;2024-08-21

2. Implementing the finite element numerical approach to optimize thermosolutal convection (TSC) energy imparted by discrete heat and solute sources in generalized Newtonian fluid flow in square enclosure;Journal of Umm Al-Qura University for Applied Sciences;2024-07-16

3. An analysis of exponential kernel fractional difference operator for delta positivity;Nonlinear Engineering;2024-01-01