On the oscillation of differential equations in frame of generalized proportional fractional derivatives

In this paper, sufficient conditions are established for the oscillation of all solutions of generalized proportional fractional differential equations of the form \begin{equation*} \left\{ \begin{array}{l} {_{a}D}^{\alpha, \rho}x(t) + \xi_1(t,x(t)) = \mu(t) + \xi_2(t,x(t)),\quad t>a \ge 0,\\[0.3cm] \lim_{t\to a^{+}} {_{a}I}^{j-\alpha, \rho}x(t) = b_j,\quad j=1,2,\ldots,n, \end{array} \right. \end{equation*}where $n = \lceil \alpha \rceil$, ${_{a}D}^{\alpha, \rho}$ is the generalized proportional fractional derivative operator of order $\alpha\in \mathbb{C}$, $Re(\alpha)\ge 0$, $0