General characteristics of a fractal Sturm—Liouville problem

ÇETİNKAYA F. A., Khalili Golmankhaneh A.

Turkish Journal of Mathematics, cilt.45, sa.4, ss.1835-1846, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 4
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3906/mat-2101-38
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1835-1846
  • Anahtar Kelimeler: eigenfunctions, eigenvalues, Fractal calculus, fractal derivative, Sturm-Liouville problem
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.