Durna, Zeynep2022-12-282022-12-282022https://doi.org/10.31801/cfsuasmas.1036073http://hdl.handle.net/20.500.12575/86535In this study, we consider a boundary value problem generated by the Sturm-Liouville equation with a frozen argument and with non-separated boundary conditions on a time scale. Firstly, we present some solutions and the characteristic function of the problem on an arbitrary bounded time scale. Secondly, we prove some properties of eigenvalues and obtain a formulation for the eigenvalues-number on a finite time scale. Finally, we give an asymptotic formula for eigenvalues of the problem on another special time scale: T = [ α , δ 1 ] ⋃ [ δ 2 , β ] .enDynamic equations, time scales, measure chains, eigenvalue problems, Sturm-Liouville theoryArticle7137207301303-5991