A Study of Positivity Analysis for Difference Operators in the Liouville–Caputo Setting-Reference-Cited by-同舟云学术

A Study of Positivity Analysis for Difference Operators in the Liouville–Caputo Setting

Published:2023-02-02 Issue:2 Volume:15 Page:391
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Srivastava Hari Mohan¹²³⁴^ORCID,Mohammed Pshtiwan Othman⁵^ORCID,Guirao Juan Luis G.⁶⁷^ORCID,Baleanu Dumitru⁸⁹¹⁰^ORCID,Al-Sarairah Eman¹¹¹²^ORCID,Jan Rashid¹³^ORCID

Affiliation:

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

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

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

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

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

6. Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, 30203 Cartagena, Spain

7. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

8. Department of Mathematics, Cankaya University, Balgat, 06530 Ankara, Turkey

9. Institute of Space Sciences, R76900 Magurele-Bucharest, Romania

10. Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, Beirut 11022801, Lebanon

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

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

13. Department of Mathematics, University of Swabi, Swabi 23561, Khyber Pakhtunkhwa, Pakistan

Abstract

The class of symmetric function interacts extensively with other types of functions. One of these is the class of positivity of functions, which is closely related to the theory of symmetry. Here, we propose a positive analysis technique to analyse a class of Liouville–Caputo difference equations of fractional-order with extremal conditions. Our monotonicity results use difference conditions ΔaLCμf(a+J0+1−μ)≥(1−μ)f(a+J0) and ΔaLCμf(a+J0+1−μ)≤(1−μ)f(a+J0) to derive the corresponding relative minimum and maximum, respectively. We find alternative conditions corresponding to the main conditions in the main monotonicity results, which are simpler and stronger than the existing ones. Two numerical examples are solved by achieving the main conditions to verify the obtained monotonicity results.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/15/2/391/pdf

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