The aim of this paper is to study the Cauchy problem for the $n$-dimensional magneto-micropolar equations with fractional dissipation. By some subtle estimates, Littlewood-Paley theory and compact method, we prove the local existence and uniqueness of the system in inhomogeneous Besov spaces under various fractional dissipation assumptions. Explicitly, we examine the existence and uniqueness of weak solutions to the $n$-dimensional $(n\geq2)$ magneto-micropolar equations with fractional dissipation $(-\Delta)^\alpha$, fractional magnetic diffusion $(-\Delta)^\beta$ and fractional spin viscosity $(-\Delta)^\gamma$, and the aim is at the uniqueness of weak solutions in the weakest possible inhomogeneous Besov spaces. We establish the local existence and uniqueness in the functional settings: i) $u_0\in{\mathcal{B}}^{1+\frac{n}{2}-2\alpha}_{2,1}(\mathbb{R}^n),\ b_0\in{\mathcal{B}}^{\frac{n}{2}}_{2,1}(\mathbb{R}^n),\ w_0\in{\mathcal{B}}^{1+\frac{n}{2}-2\gamma}_{2,1}(\mathbb{R}^n)$ with one of the following situations: $n=2,\ \alpha=1,\ \beta=0,\ \frac{1}{2}\leq\gamma<1$; $n=3,\ \alpha=1,\ \beta=0,\ \frac{1}{2}\leq\gamma<\frac{3}{2}$; $n>3,\ \alpha=1,\ \beta=0,\ \frac{1}{2}\leq\gamma<\frac{n}{2}$; $n\geq2,\ \frac{1}{2}\leq\alpha<\frac{n}{2},\ \beta\geq0,\ \alpha+\beta\geq1,\ 1\leq\gamma<\frac{n}{2}$; ii) $u_0\in{\mathcal{B}}^{1+\frac{n}{2}-2\alpha}_{2,1}(\mathbb{R}^n),\ b_0\in{\mathcal{B}}^{\frac{n}{2}}_{2,1}(\mathbb{R}^n),\ w_0\in{\mathcal{B}}^{\frac{n}{2}}_{2,1}(\mathbb{R}^n)$ with $1\leq\alpha<\frac{n}{2}$, $\beta\geq0$ and $0\leq\gamma<\frac{n}{2}$, $n\geq2$, in which we show the magneto-micropolar equations admit a unique weak solution. These results in this paper improve the known results and help us to understand more deeply the role of fractional Laplace operator in the study of hydrodynamic equations.
