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In this paper we initiate the oscillation theory for fractional differential equations. Oscillation criteria are obtained for a class of nonlinear fractional differential equations of the formwhere D q a denotes the Riemann-Liouville differential operator of order q, 0 < q ≤ 1. The results are also stated when the Riemann-Liouville differential operator is replaced by Caputo's differential operator.MSC 2010 : Primary 34A08: Secondary 34C10, 26A33

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For the 2mth order Lidstone boundary value problem,where −1 m f m → 0 ∞ is continuous, growth conditions are imposed on f which yield the existence of at least three symmetric positive solutions. This generalizes earlier papers which have applied Avery's generalization of the Leggett-Williams theorem to Lidstone problems. We then prove the analogous result for difference equations.

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