Research Article

Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator

Volume: 6 Number: 3 September 17, 2023
EN

Ambarzumyan-Type Theorem for a Conformable Fractional 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.

Keywords

Ambarzumyan-type theorem, Conformable fractional derivative, Diffusion operator, Inverse problem

References

  1. [1] V.A. Ambarzumian, Uber eine frage der eigenwerttheorie, Zeitschrift f¨ur Physik, 53 (1929), 690-695.
  2. [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. [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. [4] M. Horvath, On a theorem of Ambarzumyan, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 131 (2001), 899-907.
  5. [5] M. Kiss, An n-dimensional Ambarzumyan type theorem for Dirac operators, Inverse Problems, 20 (5)(2004), 1593-1597.
  6. [6] C.F. Yang, X.P. Yang, Some Ambarzumyan-type theorems for Dirac operators, Inverse Problems, 25 (9) (2009), 095012, 13 pages.
  7. [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. [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. [9] N.V. Kuznetsov, Generalization of a theorem of V.A. Ambarzumyan, Doklady Akademii Nauk SSSR., 146 (1962), 1259- 1262, (in Russian).
  10. [10] H.H. Chern, C.L. Shen, On the n-dimensional Ambarzumyan’s theorem, Inverse Problems, 13 (1) (1997), 15-18.
APA
Çakmak, Y. (2023). Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator. Communications in Advanced Mathematical Sciences, 6(3), 142-147. https://doi.org/10.33434/cams.1281434
AMA
1.Çakmak Y. Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator. Communications in Advanced Mathematical Sciences. 2023;6(3):142-147. doi:10.33434/cams.1281434
Chicago
Çakmak, Yaşar. 2023. “Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator”. Communications in Advanced Mathematical Sciences 6 (3): 142-47. https://doi.org/10.33434/cams.1281434.
EndNote
Çakmak Y (September 1, 2023) Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator. Communications in Advanced Mathematical Sciences 6 3 142–147.
IEEE
[1]Y. Çakmak, “Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator”, Communications in Advanced Mathematical Sciences, vol. 6, no. 3, pp. 142–147, Sept. 2023, doi: 10.33434/cams.1281434.
ISNAD
Çakmak, Yaşar. “Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator”. Communications in Advanced Mathematical Sciences 6/3 (September 1, 2023): 142-147. https://doi.org/10.33434/cams.1281434.
JAMA
1.Çakmak Y. Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator. Communications in Advanced Mathematical Sciences. 2023;6:142–147.
MLA
Çakmak, Yaşar. “Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator”. Communications in Advanced Mathematical Sciences, vol. 6, no. 3, Sept. 2023, pp. 142-7, doi:10.33434/cams.1281434.
Vancouver
1.Yaşar Çakmak. Ambarzumyan-Type Theorem for a Conformable Fractional Diffusion Operator. Communications in Advanced Mathematical Sciences. 2023 Sep. 1;6(3):142-7. doi:10.33434/cams.1281434