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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 $$D^qg(t,x_t)=f(t,x_t),\quad t\in [t_0,\infty),\tag1$$ $$x_{t_0}=\varphi,\ (t_0,\varphi)\in [0,\infty)\times \Omega,\tag2$$ where $D^q$ is Caputo’s fractional derivative of order $0 < q < 1$, $\Omega$ is an open subset of $B$ and $g,f : [t_0,\infty)\times \Omega\to \bbfR^n$ are given functionals satisfying some assumptions. Various criteria on existence and uniqueness are obtained.

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