Oscillation Theory of $h$-Fractional Difference Equations

Abstract

In this paper, we initiate the oscillation theory for $h$-fractional difference equations of the form

where $_a∆^α_h$ is the Riemann-Liouville $h$-fractional difference of order $α$, $\mathbb{T}^a_h :$={$a + kh, k ∈ \mathbb{Z}^+ $∪{0}}, and $a ≥ 0$, $h > 0$. We study the oscillation of $h$-fractional difference equations with Riemann-Liouville derivative, and obtain some sufficient conditions for oscillation of every solution. Finally, we give an example to illustrate our main results.