# American Institute of Mathematical Sciences

## 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

Received  March 2019 Revised  April 2019 Published  December 2019

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.

Citation: Raziye Mert, Thabet Abdeljawad, Allan Peterson. A Sturm-Liouville approach for continuous and discrete Mittag-Leffler kernel fractional operators. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020171
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