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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.

34A08Fractional differential equations
34B15Nonlinear boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
Full Text: DOI
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