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.
Fractal calculus, fractal derivative, Sturm-Liouville problem, eigenvalues, eigenfunctions
ÇETİNKAYA, FATMA AYÇA and GOLMANKANEH, ALIREZA KHALILI
"General characteristics of a fractal Sturm-Liouville problem,"
Turkish Journal of Mathematics: Vol. 45:
4, Article 26.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss4/26