Authors: FATMA AYÇA ÇETİNKAYA, ALIREZA KHALILI GOLMANKANEH
Abstract: In this paper, we consider a regular fractal Sturm-Liouville boundary value problem. We prove the self-adjointness of the differential operator which is generated by the $F^\alpha$-derivative introduced in . We obtained the $F^\alpha$-analogue of Liouville's theorem, and we show some properties of eigenvalues and eigenfunctions. We present examples to demonstrate the efficiency and applicability of the obtained results. The findings of this paper can be regarded as a contribution to an emerging field.
Keywords: Fractal calculus, fractal derivative, Sturm-Liouville problem, eigenvalues, eigenfunctions
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