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arXiv · 1803.05013

Sturm Liouville Equations in the frame of fractional operators with Mittag-Leffler kernels and their discrete versions

Raziye Mert·Thabet Abdeljawad·Allan Peterson
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Abstract

Very recently, some authors have studied new types of fractional derivatives whose kernels are nonsingular. In this article, we study Sturm-Liouville Equations ($SLEs$) in the frame of fractional operators with Mittag-Leffler kernels. We formulate some Fractional Sturm-Liouville Problems ($FSLPs$) with the diffferential part containing the left and right sided derivatives. We investigate the self-adjointness, eigenvalue and eigenfunction properties of the corresponding Fractional Sturm-Liouville Operators ($FSLOs$) by using fractional integration by parts formulas. The nabla discrete version of our results are also established.

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Raziye Mert, Thabet Abdeljawad, Allan Peterson. 2018-03-10. Sturm Liouville Equations in the frame of fractional operators with Mittag-Leffler kernels and their discrete versions. https://arxiv.org/abs/1803.05013

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