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

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.
 Subjects: Classical Analysis and ODEs (math.CA); Dynamical Systems (math.DS) Cite as: arXiv:1803.05013 [math.CA] (or arXiv:1803.05013v1 [math.CA] for this version)

## Submission history

From: Thabet Abdeljawad [view email]
[v1] Sat, 10 Mar 2018 06:59:03 GMT (17kb)