A Sturm-Liouville approach for continuous and discrete Mittag-Leffler kernel fractional operators

Raziye Mert; Thabet Abdeljawad; Allan Peterson

doi:10.3934/dcdss.2020171

Article Contents

2021, Volume 14, Issue 7: 2417-2434. Doi: 10.3934/dcdss.2020171

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A Sturm-Liouville approach for continuous and discrete Mittag-Leffler kernel fractional operators

1.
Mechatronic Engineering Department, University of Turkish Aeronautical Association, 06790, Ankara, Turkey
2.
Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
4.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan
5.
Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, 68588-0130, USA

^* Corresponding author: T. Abdeljawad (tabdeljawad@psu.edu.sa)
^* Corresponding author: T. Abdeljawad (tabdeljawad@psu.edu.sa)

Received: March 2019

Revised: April 2019

Early access: December 2019

Published: July 2021

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Abstract

In this work, we use integration by parts formulas derived for fractional operators with Mittag-Leffler kernels to formulate and investigate fractional Sturm-Liouville Problems ($ FSLPs $). We analyze the self-adjointness, eigenvalue and eigenfunction properties of the associated Fractional Sturm-Liouville Operators ($ FSLOs $). The discrete analogue of the obtained results is formulated and analyzed by following nabla analysis.

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Mathematics Subject Classification: 26A33, 65Q10.

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