If we have the IVP(intial value problem) for linear fractional differential equation: $$ {D}^{q}{x}\mathrm{{=}}\mathit{\lambda}{x}\mathrm{{+}}{f}\left({t}\right)\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}{x}{\mathrm{(}}{t}{\mathrm{)(}}{t}\mathrm{{-}}{t}_{0}{\mathrm{)}}^{{1}\mathrm{{-}}{q}}\left|{}\right.\mathrm{{=}}{x}_{0} $$
And we have the solution in the form:
$$ {x}{\mathrm{(}}{t}{\mathrm{)}}\mathrm{{=}}{x}^{0}{\mathrm{(}}{t}\mathrm{{-}}{t}_{0}{\mathrm{)}}^{{q}\mathrm{{-}}{1}}{E}_{q\mathrm{,}\,q}{\mathrm{(}}\mathit{\lambda}{\mathrm{(}}{t}\mathrm{{-}}{t}_{0}{\mathrm{)}}^{q}{\mathrm{)}}\mathrm{{+}}\mathop{\int}\limits_{{t}_{0}}\limits^{t}{{\mathrm{(}}{t}\mathrm{{-}}{s}{\mathrm{)}}^{{q}\mathrm{{-}}{1}}}{E}_{q\mathrm{,}\,q}\left[{\mathit{\lambda}{\mathrm{(}}{t}\mathrm{{-}}{s}{\mathrm{)}}^{q}}\right]{f}{\mathrm{(}}{s}{\mathrm{)}}{ds} $$
The solution $x(t)$ is clearly unique since the IVP satisfies the Lipschitz condition. Can someone explain to me how can we show that the solution is unique?