Relationships between the discrete Riemann-Liouville and Liouville-Caputo fractional differences and their associated convexity results-Reference-Cited by-同舟云学术

Relationships between the discrete Riemann-Liouville and Liouville-Caputo fractional differences and their associated convexity results

Published:2022 Issue:10 Volume:7 Page:18127-18141
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Guirao Juan L. G.¹²,Mohammed Pshtiwan Othman³,Srivastava Hari Mohan⁴⁵⁶⁷,Baleanu Dumitru⁸⁹¹⁰,Abualrub Marwan S.¹¹

Affiliation:

1. Departamento de Matemáca Aplicada y Estadística, Universidad Politécnica de Cartagena, ES-30202 Cartagena, Spain

2. Nonlinear Analysis and Applied Mathematics (NAAM) - Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

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

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

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

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

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

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. Mathematics Department (Prep. Program), Faculty of Science, Khalifa University, P.O. Box 127788, Abu Dhabi UAE

Abstract

<abstract><p>In this study, we have presented two new alternative definitions corresponding to the basic definitions of the discrete delta and nabla fractional difference operators. These definitions and concepts help us in establishing a relationship between Riemann-Liouville and Liouville-Caputo fractional differences of higher orders for both delta and nabla operators. We then propose and analyse some convexity results for the delta and nabla fractional differences of the Riemann-Liouville type. We also derive similar results for the delta and nabla fractional differences of Liouville-Caputo type by using the proposed relationships. Finally, we have presented two examples to confirm the main theorems.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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