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.

How to Cite this Article:
Yuqing Liu, Chengbo Zhai, Multiple positive solutions for a system of conformable fractional differential equations, Communications in Optimization Theory, Vol. 2019 (2019), Article ID 18, pp. 1-12.