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

Authors

TÜBA GÜLŞEN
EMRAH YILMAZ
HİKMET KEMALOĞLU

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.

DOI

10.3906/mat-1704-120

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