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A Sturm-Liouville approach for continuous and discrete Mittag-Leffler kernel fractional operators. (English) Zbl 1491.34018

Summary: 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.

MSC:

34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
34B24 Sturm-Liouville theory
39A12 Discrete version of topics in analysis
34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
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