General characteristics of a fractal Sturm—Liouville problem

ÇETİNKAYA F. A., Khalili Golmankhaneh A.

Turkish Journal of Mathematics, vol.45, no.4, pp.1835-1846, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2101-38
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1835-1846
  • Keywords: eigenfunctions, eigenvalues, Fractal calculus, fractal derivative, Sturm-Liouville problem
  • Van Yüzüncü Yıl University Affiliated: Yes

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 Fα -derivative introduced in [32]. We obtained the Fα -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.