Bohr radius for certain close-to-convex harmonic mappings

Let $\mathcal{H}$ be the class of harmonic functions $f=h+\bar{g}$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}:\mathrm{\mid }z\mathrm{\mid }<1\}$, where $h$ and $g$ are analytic in $\mathbb{D}$. Let $${\mathcal{P}}_{\mathcal{H}}^0(\alpha )=\{f=h+\bar{g}\in \mathcal{H}:\mathrm{\Re }(h^{\mathrm{\prime }}(z)-\alpha )>\mathrm{\mid }{g}^{\mathrm{\prime }}(z)\mathrm{\mid }with0\le \alpha <1,g^{\mathrm{\prime }}(0)=0,z\in \mathbb{D}\}$$ be the class of close-to-convex mappings defined by Li and Ponnusamy \cite{Injectivity section}. In this paper, we obtain the sharp Bohr-Rogosinski radius, improved Bohr radius and refined Bohr radius for the class ${\mathcal{P}}_{\mathcal{H}}^0(\alpha )$.