LAUSR

AbstractIn this paper, sufficient conditions are established for the oscillation of solutions of q-fractional difference equations of the form {∇0αqx(t)+f1(t,x)=r(t)+f2(t,x),t>0,limt→0+qI0j−αx(t)=bj(j=1,2,…,m),$$ \left \{ \textstyle\begin{array}{l} {}_{q}\nabla_{0}^{\alpha}x(t)+f_{1}(t,x)=r(t)+f_{2}(t,x), \quad t>0 ,\\ \lim_{t \to0^{+}}{{}_{q}I_{0}^{j-\alpha}x(t)}=b_{j} \quad(j=1,2,\ldots,m), \end{array}\displaystyle \right . $$ where m=⌈α⌉$m=\lceil\alpha\rceil$, ∇0αq${}_{q}\nabla_{0}^{\alpha}$ is the Riemann-Liouville q-differential operator and I0m−αq${}_{q}I_{0}^{m-\alpha}$ is the q-fractional integral. The results are also obtained when the Riemann-Liouville q-differential operator is replaced by Caputo q-fractional difference. Examples are provided to demonstrate the effectiveness of the main result.