Positivity analysis for the discrete delta fractional differences of the Riemann-Liouville and Liouville-Caputo types-Reference-Cited by-同舟云学术

Positivity analysis for the discrete delta fractional differences of the Riemann-Liouville and Liouville-Caputo types

Published:2022 Issue:8 Volume:30 Page:3058-3070
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Mohammed Pshtiwan Othman¹,Srivastava Hari Mohan²³⁴⁵,Baleanu Dumitru⁶⁷⁸,Elattar Ehab E.⁹,Hamed Y. S.¹⁰

Affiliation:

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

2. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada

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

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

5. Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy

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

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

8. Lebanese American University, 11022801 Beirut, Lebanon

9. Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

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

Abstract

<abstract><p>In this article, we investigate some new positivity and negativity results for some families of discrete delta fractional difference operators. A basic result is an identity which will prove to be a useful tool for establishing the main results. Our first main result considers the positivity and negativity of the discrete delta fractional difference operator of the Riemann-Liouville type under two main conditions. Similar results are then obtained for the discrete delta fractional difference operator of the Liouville-Caputo type. Finally, we provide a specific example in which the chosen function becomes nonincreasing on a time set.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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