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Zbl 1204.34007
Goodrich, Christopher S.
Existence of a positive solution to a class of fractional differential equations. (English)
[J] Appl. Math. Lett. 23, No. 9, 1050-1055 (2010). ISSN 0893-9659

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.
[Juan J. Trujillo (La Laguna)]

MSC 2000:: *34A08
34B15 Nonlinear boundary value problems of ODE
34B18 Positive solutions of nonlinear boundary value problems

Keywords: fractional calculus; fractional boundary value problem; Green's function; fixed point theorem in cones; Riemann-Liouville derivative

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Zentralblatt MATH Berlin [Germany]