SPECTRAL EXPANSION FOR CONFORMABLE FRACTIONAL STURM-LIOUVILLE PROBLEM ON THE WHOLE LINE

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Allahverdİev B. P., Tuna H., Yalçinkaya Y.

Kragujevac Journal of Mathematics, vol.48, no.6, pp.811-826, 2024 (ESCI, Scopus)

  • Publication Type: Article / Article
  • Volume: 48 Issue: 6
  • Publication Date: 2024
  • Doi Number: 10.46793/kgjmat2406.811a
  • Journal Name: Kragujevac Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.811-826
  • Keywords: Parseval equality, Singular conformable fractional Sturm-Liouville equation, spectral expansion, spectral function
  • Open Archive Collection: AVESIS Open Access Collection
  • Süleyman Demirel University Affiliated: Yes

Abstract

In this article, we discuss a conformable fractional Sturm-Liouville boundary-value problem on the whole line. We prove the existence of a spectral function for the singular conformable fractional Sturm-Lioville problem. Further, we establish a Parseval equality and spectral expansion formula by terms of the spectral function for conformable fractional Sturm-Liouville problem on the whole line.