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Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay. (English) Zbl 1191.34098

Summary: We deal with the mild solution for fractional semilinear differential equations with infinite delay:

D α x(t)=Ax(t)+f(t,x t ,Bx(t)),t[0,T],

x(t)=φ(t), t]-,0[ with T>0 and 0<α<1. We prove the existence (and uniqueness) of solutions, assuming that A generates an α-resolvent family (S α (t))t0 on a complex Banach space 𝕏 by means of classical fixed points methods.


MSC:
34K37Functional-differential equations with fractional derivatives
34K40Neutral functional-differential equations
34K30Functional-differential equations in abstract spaces
47N20Applications of operator theory to differential and integral equations
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