Conformable fractional Sturm-Liouville equation

Allahverdiev B., Tuna H., YALCİNKAYA Y.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.42, no.10, pp.3508-3526, 2019 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 42 Issue: 10
  • Publication Date: 2019
  • Doi Number: 10.1002/mma.5595
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3508-3526
  • Keywords: conformable fractional Sturm-Liouville operator, eigenfunction expansions, eigenvalues and eigenfunctions, Green's function, self-adjoint operator, CALCULUS
  • Süleyman Demirel University Affiliated: Yes

Abstract

In this article, we discuss a conformable fractional Sturm-Liouville boundary-value problem. We prove an existence and uniqueness theorem for this equation and formulate a self-adjoint boundary value problem. We also construct the associated Green function of this problem, and we give the eigenfunction expansions. Finally, we will give some examples.