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Zbl 1061.34001
Bai, Chuan-zhi; Fang, Jin-xuan
The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations.
(English)
[J] Appl. Math. Comput. 150, No. 3, 611-621 (2004). ISSN 0096-3003

The authors discuss the existence of a positive solution to the singular coupled system $$D^s u= f(t,v), \quad D^pv= g(t, u),\quad 0< t< 1,\tag1$$ where $0< s< 1$, $0< p< 1$, $D^s$ and $D^p$ are two standard Riemann-Liouville fractional derivatives, $f,g: (0,1]\times [0,+\infty)\to [0,+\infty)$ are two given continuous functions. The proof of the existence result for (1) is based on some kind of fixed-point theorem in cones.
[Messoud A. Efendiev (Berlin)]
MSC 2000:
*34A12 Initial value problems for ODE
26A33 Fractional derivatives and integrals (real functions)

Keywords: singular nonlinear fractional differential equation; positive solution; fixed-point theorem in cones

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