## 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
$D^qg(t,x_t)=f(t,x_t),\quad t\in [t_0,\infty),\tag{1}$
$x_{t_0}=\varphi,\;(t_0,\varphi)\in [0,\infty)\times \Omega,\tag{2}$
where $$D^q$$ is Caputo’s fractional derivative of order $$0 < q < 1$$, $$\Omega$$ is an open subset of $$B$$ and $$g,f : [t_0,\infty)\times \Omega\to \mathbb{R}^n$$ are given functionals satisfying some assumptions. Various criteria on existence and uniqueness are obtained.

### MSC:

 34K05 General theory of functional-differential equations 26A33 Fractional derivatives and integrals 34K40 Neutral functional-differential equations
Full Text:

### References:

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