In this paper, we consider the Cauchy problem of d-dimensional magnetohydrodynamics equations \((d\ge 2)\) with fractional dissipation \((-\Delta )^{\alpha }u\) and fractional magnetic diffusion \((-\Delta )^{\beta }b.\) The aim of this paper is to establish the uniqueness of weak solutions under the \(L^p\) framework in sense of the weakest possible inhomogeneous Besov spaces. We obtain the local existence and uniqueness in the functional setting \(u\in L_T^{\infty }(B_{p,1}^{\frac{d}{p}+1-2\alpha }({\mathbb {R}}^d))\) and \(b\in L_T^{\infty }(B_{p,1}^{\frac{d}{p}}({\mathbb {R}}^d))\) when \(\alpha \) and \(\beta \) satisfy certain conditions by using the iterative scheme and compactness arguments.
