KaydedilenlerDerginizi ekleyin

Dergiler / Communications in Advanced Mathematical Sciences / 2023 / Cilt: 6 Sayı: 3

Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator

Yaşar ÇAKMAK
Sayfa
142–147
Yayın Tarihi
2023-09-17
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this paper, we prove an Ambarzumyan-type theorem for a Conformable fractional diffusion operator, i.e. we show that $q(x)$ and $p(x)$ functions are zero if the eigenvalues are the same as the eigenvalues of zero potentials.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we prove an Ambarzumyan-type theorem for a Conformable fractional diffusion operator, i.e. we show that $q(x)$ and $p(x)$ functions are zero if the eigenvalues are the same as the eigenvalues of zero potentials.
📊
Temel Bulgular & Veri:In this paper, we prove an Ambarzumyan-type theorem for a Conformable fractional diffusion operator, i.e. we show that $q(x)$ and $p(x)$ functions are zero if the eigenvalues are the same as the eigenvalues of zero potentials.
💡
Sonuç & Katkı:In this paper, we prove an Ambarzumyan-type theorem for a Conformable fractional diffusion operator, i.e. we show that $q(x)$ and $p(x)$ functions are zero if the eigenvalues are the same as the eigenvalues of zero potentials.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Ambarzumyan-type theorem · Conformable fractional derivative · Diffusion operator

Abstract

In this paper, we prove an Ambarzumyan-type theorem for a Conformable fractional diffusion operator, i.e. we show that $q(x)$ and $p(x)$ functions are zero if the eigenvalues are the same as the eigenvalues of zero potentials.

🔖

Bu Makaleye Atıf Yap

ÇAKMAK, Y. (2023). Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator. Communications in Advanced Mathematical Sciences, Cilt: 6 Sayı: 3, 142–147. https://ajindex.com/articles/962117

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (18)

  1. V.A. Ambarzumian, Uber eine frage der eigenwerttheorie, Zeitschrift f¨ur Physik, 53 (1929), 690-695
  2. H.H. Chern, C.K. Law, H.J. Wang, Extensions of Ambarzumyan’s theorem to general boundary conditions, J. Math. Anal. Appl., 263 (2001), 333-342. Corrigendum: J. Math. Anal. Appl., 309 (2) (2005), 764-768
  3. E.M. Harrell, On the extension of Ambarzunyan’s inverse spectral theorem to compact symmetric spaces, Amer. J. Math., 109 (1987), 787-795
  4. M. Horvath, On a theorem of Ambarzumyan, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 131 (2001), 899-907
  5. M. Kiss, An n-dimensional Ambarzumyan type theorem for Dirac operators, Inverse Problems, 20 (5)(2004), 1593-1597
  6. C.F. Yang, X.P. Yang, Some Ambarzumyan-type theorems for Dirac operators, Inverse Problems, 25 (9) (2009), 095012, 13 pages
  7. C.F. Yang, Z.Y. Huang, X.P. Yang, Ambarzumyan’s theorems for vectorial Sturm-Liouville systems with coupled boundary conditions, Taiwanese J. Math., 14 (4) (2010), 1429-1437
  8. C.L. Shen, On some inverse spectral problems related to the Ambarzumyan problem and the dual string of the string equation, Inverse Problems, 23 (6) (2007), 2417-2436
  9. N.V. Kuznetsov, Generalization of a theorem of V.A. Ambarzumyan, Doklady Akademii Nauk SSSR., 146 (1962), 1259- 1262, (in Russian)
  10. H.H. Chern, C.L. Shen, On the n-dimensional Ambarzumyan’s theorem, Inverse Problems, 13 (1) (1997), 15-18
  11. C.F. Yang, X.P. Yang, Ambarzumyan’s theorem with eigenparameter in the boundary conditions, Acta Math. Sci., 31 B(4) (2011), 1561-1568
  12. V.A. Yurko, On Ambarzumyan-type theorems, Appl. Math. Lett., 26 (4) (2013), 506-509
  13. K. Marton, An n-dimensional Ambarzumyan type theorem for Dirac operators, Inverse Problems, 20 (5) (2004), 1593-1597
  14. A.A. Kırac, Ambarzumyan’s theorem for the quasi-periodic boundary conditions, Anal. Math. Phys., 6 (2016), 297-300
  15. H. Koyunbakan, D. Lesnic, E.S. Panakhov, Ambarzumyan type theorem for a quadratic Sturm-Liouville operator, Turkish Journal of Sciences and Technology, 8 (1) (2013), 1-5
  16. G. Freiling, V.A. Yurko, Inverse Sturm-Liouville Problems and Their Applications, Nova Science Publishers, New York, 2001
  17. E. Yilmaz, H. Koyunbakan, Some Ambarzumyan type theorems for Bessel operator on a finite interval, Differ. Equ. Dyn. Syst., 27 (4) (2019), 553–559
  18. R. Khalil, M. Al Horania, A. Yousefa, et al., A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014),