Summary: We investigate global uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces. We shall rely on a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to M. Frigon
and A. Granas
[Ann. Sci. Math. Qué. 22, No. 2, 161–168 (1998; Zbl 1100.47514
)]. The results are obtained by using the
on a complex Banach space
combined with the above-mentioned fixed point theorem. As an application, a controllability result with one parameter is also provided to illustrate the theory.