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 \[ D^s u= f(t,v), \quad D^pv= g(t, u),\quad 0< t< 1,\tag{1} \] 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.


34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
26A33 Fractional derivatives and integrals
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