Based on an equivalent derivative nonlinear Schr\”{o}inger equation, some periodic and non-periodic two-parameter solutions of the deformed continuous Heisenberg spin equation are obtained. These solutions are all proved to be ill-posed by the estimates of Fourier integral in ${H}^{s}_{\mathrm{S}^{2}}$ (periodic solution in ${H}^{s}_{\mathrm{S}^{2}}(\mathbb{T})$ and non-periodic solution in ${H}^{s}_{\mathrm{S}^{2}}(\mathbb{R})$ respectively). If $\alpha \neq 0$, the range of the weak ill-posedness index is $1

In this paper, the differentiability on time and continuity on fractional order of solutions for a class of Caputo fractional evolution equations are studied. Under appropriate assumptions, the existence and differentiability on time of solutions for linear as well as semilinear Caputo fractional evolution equations are analyzed, the continuity of solutions on fractional order for linear and semilinear Caputo fractional evolution equations are discussed. In addition, if the fractional order converges to $1$, then the solutions of the Caputo fractional differential equations become the solutions of classic evolution equations. The continuity of solutions on fractional order for some fractional systems is numerically studied, and the results are basically consistent with the theoretical results.