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Existence results for fractional order functional differential equations with infinite delay. (English) Zbl 1209.34096

The paper deals with the existence of solutions for initial value problems for fractional-order functional differential equations with infinite delay

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

and

D α [y(t)-g(t,y t )]=f(t,y t ),tJ=[0,b],
y(t)=φ(t),t(-,0],

where D α is the standard Riemann-Liouville fractional derivative. The Banach fixed point theorem and a nonlinear alternative of Leray-Schauder type are used to investigate the given initial value problems.

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