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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
\[ D^\alpha y(t)=f(t,y_t),\quad t\in J=[0,b],\quad 0<\alpha<1, \]
\[ y(t)=\varphi(t),\quad t\in (-\infty,0] \]
and
\[ D^\alpha[y(t)-g(t,y_t)]=f(t,y_t),\quad t\in J=[0,b], \]
\[ y(t)=\varphi(t),\quad t\in (-\infty,0], \]
where \(D^\alpha\) 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:
34K37 Functional-differential equations with fractional derivatives
34K40 Neutral functional-differential equations
47N20 Applications of operator theory to differential and integral equations
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