#### Yuqing Liu, Chengbo Zhai, Multiple positive solutions for a system of conformable fractional differential equations, Vol. 2019 (2019), Article ID 18, pp. 1-12

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DOI: 10.23952/cot.2019.18

Received April 7, 2019; Accepted December 11, 2019; December 27, 2019

Abstract. In this paper, we discuss a new  system of  conformable fractional differential equations
$T_{\alpha}x(t)+a(t) f(t,y(t))=0,\ t\in(0,1),$
$T_{\beta}y(t)+b(t) g(t,x(t))=0,\ t\in(0,1),$
$x(0)=0,x(1)=\mu\int_{0}^{1}x(t)dt,\ \mu\in[0,2),$
$y(0)=0,y(1)=\nu\int_{0}^{1}y(t)dt,\ \nu\in[0,2),$
where  $\alpha,\beta\in(1,2]$, $T_{\alpha}$ and $T_{\beta}$ are the conformable fractional derivatives of orders $\alpha$ and $\beta$. By using the fixed point index theory, we obtain the existence of single and multiple  positive solutions  to  the conformable fractional differential system. Moreover, we give two concrete examples to illustrate  our main results.