In this paper, we study the algebraic structure of $(σ,δ)$-polycyclic codes, defined as submodules in the quotient module $S/Sf$, where $S=R[x,σ,δ]$ is the Ore extension ring, $f\in S$, and $R$ is a finite but not necessarily commutative ring. We establish that the Euclidean duals of $(σ,δ)$-polycyclic codes are $(σ,δ)$-sequential codes. By using $(σ,δ)$-Pseudo Linear Transformation, we define the annihilator dual of $(σ,δ)$-polycyclic codes. Then, we demonstrate that the annihilator duals of $(σ,δ)$-polycyclic codes maintain their $(σ,δ)$-polycyclic nature. Furthermore, we classify when two $(σ,δ)$-polycyclic codes are Hamming isometrical equivalent. By employing Wedderburn polynomials, we introduce simple-root $(σ,δ)$-polycyclic codes. Subsequently, we define the $(σ, δ)$-Mattson-Solomon transform for this class of codes and we address the problem of decomposing these codes by using the properties of Wedderburn polynomials.