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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a b s t r a c tIn this work, we are concerned with oscillation of third-order nonlinear functional differential equations of the formBy using a Riccati type transformation and integral averaging technique, we establish some new sufficient conditions under which every solution y(t) either oscillates or converges to zero as t → ∞.Unlike ones from the known works in the literature, our results are applicable to nonlinear functional differential equations of the above form when f (u) = |u| α−1 u, α > 0.

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The efficient technique of expanding the wave function into aFourier᎐Bessel series to solve the radial Schrodinger equation with polynomial potentials, Ž .that the spectra of two-and three-dimensional oscillators cover the spectra of the corresponding N-dimensional problems for all N. Extremely accurate numerical results are presented for illustrative purposes. The connection between the eigenvalues of the Ž . general anharmonic oscillators and the confinement potentials of the form V r s yZrr q Ý Ky1 c r i is also discussed.