LAUSR

AbstractIn this paper, we consider the oscillation theory for fractional differential equations. We obtain oscillation criteria for three classes of fractional differential equations of the forms Tαt0x(t)+∑i=1mpi(t)x(τi(t))=0,t⩾t0,Tαt0(r(t)(Tαt0(x(t)+p(t)x(τ(t))))β)+q(t)xβ(σ(t))=0,t⩾t0, $$\begin{aligned}& T_{\alpha}^{t_{0}} x(t)+\sum_{i=1}^{m}p_{i}(t)x \bigl(\tau_{i}(t)\bigr)=0,\quad t\geqslant t_{0}, \\& T_{\alpha}^{t_{0}} \bigl(r(t) \bigl(T_{\alpha}^{t_{0}} \bigl(x(t)+p(t)x\bigl(\tau(t)\bigr)\bigr)\bigr)^{\beta}\bigr)+q(t)x^{\beta}\bigl(\sigma(t)\bigr)=0, \quad t\geqslant t_{0}, \end{aligned}$$ and Tαt0(r2Tαt0(r1(Tαt0y)β))(t)+p(t)(Tαt0y(t))β+q(t)f(y(g(t)))=0,t⩾t0,$$T_{\alpha}^{t_{0}}\bigl(r_{2}T_{\alpha}^{t_{0}} \bigl(r_{1}\bigl(T_{\alpha}^{t_{0}} y \bigr)^{\beta}\bigr)\bigr) (t)+p(t) \bigl(T_{\alpha}^{t_{0}} y(t)\bigr)^{\beta}+q(t)f\bigl(y\bigl(g(t)\bigr)\bigr)=0, \quad t \geqslant t_{0}, $$ where Tα$T_{\alpha}$ denotes the conformable differential operator of order α, 0