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Theory and Modern Applications

Erratum to: Existence of mild solutions for fractional nonlocal evolution equations with delay in partially ordered Banach spaces

The Original Article was published on 10 January 2017

In the publication of this article [1], there was an error in Chapter 4 Application on page 9. The error:

$$h\bigl(t,y,x_{t}(\tau,y)\bigr) \textstyle\begin{cases} 1, & \mbox{if } x\leq 0,\\ 1+2x_{t} (\tau,y), & \mbox{if } 0< x< 2,\\ 5, & \mbox{if } 0\geq 2, \end{cases}\displaystyle \qquad g(x) (y) \textstyle\begin{cases} 1, & \mbox{if } x\leq 0,\\ 1+\frac{x(t,y)}{1+x(t,y)}, & \mbox{if } x>0. \end{cases} $$

Instead should indicate:

$$h\bigl(t,y,x_{t}(\tau,y)\bigr)= \textstyle\begin{cases} 1, & \mbox{if } x\leq 0,\\ 1+2x_{t} (\tau,y), & \mbox{if } 0< x< 2,\\ 5, & \mbox{if } 0\geq 2, \end{cases}\displaystyle \qquad g(x) (y)= \textstyle\begin{cases} 1, & \mbox{if } x\leq 0,\\ 1+\frac{x(t,y)}{1+x(t,y)}, & \mbox{if } x>0. \end{cases} $$

This has now been included in the original article and the erratum.

References

  1. Liang, Y, Yang, H, Guo, K: Existence of mild solutions for fractional nonlocal evolution equations with delay in partially ordered Banach spaces. Bound. Value Probl. 2017, 11 (2017). doi:10.1186/s13662-016-1058-1

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Correspondence to Yue Liang.

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The online version of the original article can be found under doi:10.1186/s13662-016-1058-1.

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Liang, Y., Yang, H. & Gou, K. Erratum to: Existence of mild solutions for fractional nonlocal evolution equations with delay in partially ordered Banach spaces. Adv Differ Equ 2017, 40 (2017). https://doi.org/10.1186/s13662-017-1100-y

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  • DOI: https://doi.org/10.1186/s13662-017-1100-y