Inverse nodal problem for a conformable fractional diffusion operator

ÇAKMAK Y.

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, cilt.29, sa.9, ss.1308-1322, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 9
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1080/17415977.2020.1847103
  • Dergi Adı: INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1308-1322
  • Anahtar Kelimeler: Diffusion operator, inverse nodal problem, conformable fractional, DIFFERENTIAL PENCIL, POINTS
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

In this paper, a second order differential pencil, namely diffusion equation with Dirichlet boundary conditions which includes conformable fractional derivatives of order alpha(0 < alpha <= 1) instead of the ordinary derivatives in a traditional diffusion operator, is considered. Firstly, the asymptotic formulae of eigenvalues and eigenfunctions of the operator are obtained. Secondly, the nodal points which are the zeros of the eigenfunction of the operator are investigated. Later, an effective procedure for solving the inverse nodal problem is given and thus the potentials of the diffusion operator are reconstructed with the help of a dense subset of nodal points. Finally, an example to illustrate the theoretical findings of this study is presented.