This article deals with the mathematical analysis of the inverse problem of identifying the distinguishability of input-output mappings in the linear time fractional inhomogeneous parabolic equation $D_{t}^{\alpha}u(x,t)=(k(x)u_{x})_{x}+r(t)F(x,t)$ , $0<\alpha\leq 1$ , with mixed boundary conditions $u(0,t)=\psi_{0}(t)$ , $u_{x}(1,t)=\psi_{1}(t)$ . By defining the input-output mappings $\Phi[\cdot]:\mathcal{K}\rightarrow C^{1}[0,T]$ and $\Psi[\cdot]:\mathcal{K}\rightarrow C[0,T]$ the inverse problem is reduced to the problem of their invertibility. Hence, the main purpose of this study is to investigate the distinguishability of the input-output mappings $\Phi[\cdot]$ and $\Psi[\cdot]$ . Moreover, the measured output data $f(t)$ and $h(t)$ can be determined analytically by a series representation, which implies that the input-output mappings $\Phi[\cdot]:\mathcal{K}\rightarrow C^{1}[0,T]$ and $\Psi[\cdot]:\mathcal{K}\rightarrow C[0,T]$ can be described explicitly, where $\Phi[r]=k(x)u_{x}(x,t;r)|_{x=0}$ and $\Psi [r]=u(x,t;r)|_{x=1}$ . Also, numerical tests using finite difference scheme combined with an iterative method are presented.