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Existence of a positive solution to a class of fractional differential equations. (English) Zbl 1204.34007
The author considers a class of fractional boundary value problem involving the Riemann-Liouville derivative. The main contribution of the author is to improve certain recent results by showing that the Green function associated to the mentioned problem satisfies, among other properties, a Harnack-like inequality. Also, the author shows that the mentioned boundary problem has a positive solution under standard assumptions on the nonlinearity part of the fractional differential equation.

MSC:
34A08 Fractional ordinary differential equations and fractional differential inclusions
34B15 Nonlinear boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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