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Existence and uniqueness for fractional neutral differential equations with infinite delay. (English) Zbl 1177.34084

Summary: We consider the Cauchy initial value problem of fractional neutral functional differential equations with infinite delay of the form

D q g(t,x t )=f(t,x t ),t[t 0 ,),(1)
x t 0 =ϕ,(t 0 ,ϕ)[0,)×Ω,(2)

where D q is Caputo’s fractional derivative of order 0<q<1, Ω is an open subset of B and g,f:[t 0 ,)×Ω n are given functionals satisfying some assumptions. Various criteria on existence and uniqueness are obtained.

MSC:
34K05General theory of functional-differential equations
26A33Fractional derivatives and integrals (real functions)
34K40Neutral functional-differential equations