In this paper, we investigate the n-dimensional incompressible magnetohydrodynamic (MHD) equations with fractional dissipation and magnetic diffusion. Firstly, employing energy methods, we demonstrate that if the initial data is sufficiently small in \(H^s(\mathbb {R}^n)\) with \(s=1+\frac{n}{2}-2\alpha ~(0<\alpha <1)\) , then the system possesses a global solution. In order to establish the uniqueness, we enhance the regularity of the initial data and prove that if \((u_0,b_0)\) is small in \(H^s(\mathbb {R}^n)\) with \(s=1+\frac{n}{2}-\alpha ~(0<\alpha <1)\) , then the system admits a unique global solution. Secondly, by applying frequency decomposition, we obtain \(\Vert u,b\Vert _{L^2}\rightarrow 0,~t\rightarrow \infty \) . Assuming in addition that the initial data \(u_0,b_0\in L^p(1\le p<2)\) , we establish optimal decay estimates for the solutions and their higher order derivatives by employing a more refined frequency decomposition approach. In the case \(\alpha = 0\) , the system corresponds to a damped MHD equations, which have been previously investigated in [34]. Our results improve ones in [34] by extending the solution space from \(H^s(s>\frac{n}{2}+1)\) to \(B^s_{2,1}(s\ge \frac{n}{2}+1)\) .
