Abstract
In this paper, we define a Fractional Sturm-Liouville Operator (FSLO), introduce a regular Fractional Sturm-Liouville Problem (FSLP), and investigate the properties of the eigenfunctions and the eigenvalues of the operator. We demonstrate that these properties are similar and in some cases identical to those for Integer Sturm-Liouville Operator. We briefly introduce a Reflected Fractional Sturm-Liouville Operator (RFSLO) and demonstrate that neither the FSLO nor the RFSLO are symmetric. We shall consider the topic of reflection symmetry in a subsequent paper.
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