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Zbl 1209.34096
Benchohra, M.; Henderson, J.; Ntouyas, S.K.; Ouahab, A.
Existence results for fractional order functional differential equations with infinite delay. (English)
[J] J. Math. Anal. Appl. 338, No. 2, 1340-1350 (2008). ISSN 0022-247X

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.
[Zdeněk Šmarda (MR2386501)]

MSC 2000:: *34K37
34K40 Neutral equations
47N20 Appl. of operator theory to differential and integral equations

Keywords: functional differential equations; fractional derivative; fractional integral; existence; fixed point

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