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Uniqueness results for fractional functional differential equations with infinite delay in Fréchet spaces. (English) Zbl 1175.34080

The paper is concerned with the existence and uniqueness of a solution to an initial value problem for functional differential equations with unbounded delay and fractional order of the form:

D α [y(t)-g(t,y t )]=f(t,y t ),0<α<1,t[0,),y(t)=φ(t),t(-,0]·

The main tool of proving the results is the nonlinear Leray-Schauder type alternative for contractive mappings in Fréchet spaces due to M. Frigon and A. Granas [Ann. Sci. Math. Qué. 22, No. 2, 161–168 (1998; Zbl 1100.47514)].

MSC:
34K05General theory of functional-differential equations
26A42Integrals of Riemann, Stieltjes and Lebesgue type (one real variable)
26A33Fractional derivatives and integrals (real functions)
47N20Applications of operator theory to differential and integral equations