Conformable fractional Sturm–Liouville equation and some existence results on time scales

Abstract

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