Conformable fractional Sturm-Liouville equation and some existenceresults on time scales

Authors

TÜBA GÜLŞEN
EMRAH YILMAZ
HİKMET KEMALOĞLU

DOI

10.3906/mat-1704-120

Abstract

In this study, we analyze a conformable fractional (CF) Sturm-Liouville (SL) equation with boundary conditions on an arbitrary time scale $\mathbb{T}$. Then we extend the basic spectral properties of the classical SL equation to the CF case. Finally, some sufficient conditions are established to guarantee the existence of a solution for this CF-SL problem on $\mathbb{T}$ by using certain fixed point theorems. For explaining these existence theorems, we give an example with appropriate choices.

Keywords

Time scale calculus, conformable fractional derivative, existence theorem

First Page

1348

Last Page

1360

Recommended Citation

GÜLŞEN, TÜBA; YILMAZ, EMRAH; and KEMALOĞLU, HİKMET (2018) "Conformable fractional Sturm-Liouville equation and some existenceresults on time scales," Turkish Journal of Mathematics: Vol. 42: No. 3, Article 48. https://doi.org/10.3906/mat-1704-120
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/48