A Kamenev-type oscillation result for a linear $(1+\alpha )$--order fractional differential equation

Abstract

We investigate the eventual sign changing for the solutions of the linear equation ${\left(x^{(\alpha )}\right)}^{\prime }+q(t)x=0$, $t\ge 0$, when the functional coefficient $q$ satisfies the Kamenev-type restriction $\underset{t\to +\infty }{\mathrm{limsup}}\frac{1}{t^{\epsilon }}{\int }_{t_0}^t(t-s{)}^{\epsilon }q(s)ds=+\infty$ for some $\epsilon >2$, $t_0>0$. The operator $x^{(\alpha )}$ is the Caputo differential operator and $\alpha \in (0,1)$.