The construction of Hom left-symmetric conformal bialgebras

In this paper, we first introduce the notion of Hom-left-symmetric conformal bialgebras and show some nontrivial examples. Also, we present construction methods of matched pairs of Hom-Lie conformal algebras and Hom-left-symmetric conformal algebras. Finally, we prove that a finite Hom-left-symmetric conformal bialgebra is free as a $\mathbb{C}[\mathrm{\partial }]$-module is equivalent to a Hom-parak"{a}hler Lie conformal algebra. In particular, we investigate the coboundary Hom-left-symmetric conformal bialgebras.