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Positive solutions for boundary value problem of nonlinear fractional functional differential equations. (English) Zbl 1223.34107

Summary: In this paper, we investigate the existence of positive solutions for the nonlinear Caputo fractional order functional differential equation

${D}_{0+}^{\alpha }u\left(t\right)+a\left(t\right)f\left({u}_{t}\right)=0,\phantom{\rule{1.em}{0ex}}0

where ${D}_{0+}^{\alpha }$ is the Caputo fractional order derivative, subject to the boundary conditions

$-au\left(t\right)+b{u}^{\text{'}}\left(t\right)=\xi \left(t\right),\phantom{\rule{1.em}{0ex}}-\tau \le t\le 0,$
$cu\left(t\right)+d{u}^{\text{'}}\left(t\right)=\eta \left(t\right),\phantom{\rule{1.em}{0ex}}1\le t\le 1+\beta ,$

we obtain the existence results of positive solutions by using some fixed point theorems.

##### MSC:
 34K37 Functional-differential equations with fractional derivatives 34K10 Boundary value problems for functional-differential equations
##### References:
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