On global solutions to fractional functional differential equations with infinite delay in Fréchet spaces

Abstract

In this paper, 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 Frigon and Granas. The results are obtained by using the α -resolvent family ( S α ( t ) ) t ≥ 0 on a complex Banach space X combined with the above-mentioned fixed point theorem. As an application, a controllability result with one parameter is also provided to illustrate the theory.