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The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations. (English) Zbl 1061.34001

The authors discuss the existence of a positive solution to the singular coupled system

${D}^{s}u=f\left(t,v\right),\phantom{\rule{1.em}{0ex}}{D}^{p}v=g\left(t,u\right),\phantom{\rule{1.em}{0ex}}0

where $0, $0, ${D}^{s}$ and ${D}^{p}$ are two standard Riemann-Liouville fractional derivatives, $f,g:\left(0,1\right]×\left[0,+\infty \right)\to \left[0,+\infty \right)$ are two given continuous functions. The proof of the existence result for (1) is based on some kind of fixed-point theorem in cones.

##### MSC:
 34A12 Initial value problems for ODE, existence, uniqueness, etc. of solutions 26A33 Fractional derivatives and integrals (real functions)