Given the solution $f$ of the sequential fractional differential equation $_{ a}D_{ t}^{ \alpha}(_{ a}D_{ t}^{ \alpha}f)+P(t)f=0$, $t\in[b,c]$, where $-\infty<a<b<c<+\infty$, $\alpha\in({ 1/2},1)$ and $P:[a,+\infty)\to[0,P_{ \infty}]$, $P_{ \infty}<+\infty$, is continuous, assume that there exist $t_1,t_2\in[b,c]$ such that $f(t_1)=(_{ a}D_{ t}^{ \alpha}f)(t_2)=0$. Then, we establish here a positive lower bound for $c-a$ which depends solely on $\alpha,P_{ \infty}$. Such a result might be useful in discussing disconjugate fractional differential equations and fractional interpolation, similarly to the case of (integer order) ordinary differential equations.
Categories: math.DS math-ph math.MP