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.


34A08 Fractional ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
Full Text: DOI


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