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We deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay: D&#x03B1;x(t)+Ax(t)=f(t,xt), t&#x2208;[0,T], x(t)=&#x03D5;(t), t&#x2208;]&#x2212;&#x221E;,0], with T&#x003E;0 and 0&#x003C;&#x03B1;&#x003C;1. We prove the existence (and uniqueness) of solutions, assuming that &#x2212;A is a linear closed operator which generates an analytic semigroup (T(t))t&#x2265;0 on a Banach space &#x1D54F; by means of the Banach&#39;s fixed point theorem. This generalizes some recent results

A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay