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 boundary conditions on an arbitrary time scale 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 T by using certain fixed point theorems. For explaining these existence theorems, we give an example with appropriate choices.