SOME OSCILLATION RESULTS FOR TWO RIEMANN–LIOUVILLE FRACTIONAL DYNAMIC EQUATIONS ON TIME SCALES

In this paper, we initially study oscillation of Riemann–Liouville fractional dynamic equations on time scales. By use of the properties of Riemann–Liouville fractional integral and fractional derivative on arbitrary time scales, we initially establish some oscillation criteria for two classes of Riemann–Liouville fractional dynamic equations on time scales. These results unify the fractional continuous and discrete analysis, and are generalizations of many existing results in the literature. Several critical inequalities and Riccati transformation technique as well as integral technique are used in the deduction process. For testing the oscillation results, we propose some examples. The process for establishing the main oscillation criteria can be extended to other types of Riemann–Liouville fractional dynamic equations on time scales with complex forms.