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

Authors : Tüba Gülşen, Emrah Yilmaz, Hikmet Kemaloğlu

Pages : 1348-1360

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Publication Date : 9999-12-31

Article Type : Makaleler

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