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On global solutions to fractional functional differential equations with infinite delay in Fréchet spaces. (English) Zbl 1228.34015
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 α-resolvent family (S α (t)) t0 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.
MSC:
34A08Fractional differential equations
47H10Fixed point theorems for nonlinear operators on topological linear spaces
34K99Functional-differential equations
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