The time-domain Maxwell equations in cylindrical coordinates are transformed to AH domain using a AH

differential operator technology [6].

To factorize Schrodinger equation, there are pairs of linear

differential operator as

The convergence of series (21) depends on the nonlinear

differential operator n.

The first one is defined by the restriction of the quadratic form associated with operator (1) to the subspace of functions of the form w([x.sub.1])[u.sub.1]([x.sub.2]), where [u.sub.1] is the first eigenfunction of the one-dimensional

differential operator on [L.sup.2]((0, a)) and, hence, is reduced to a well studied one-dimensional Schroodinger operator with the potential equal to a weighted mean value [??] of V over (0, a).

Let us define the second-order

differential operator [L.sup.2.sub.[alpha]]: [C.sup.2](0, [infinity]) [right arrow] C(0, [infinity]) by

In this paper, we consider the

differential operator [mathematical expression not reproducible], (1.1) be a degenerate non- selfadjoint

differential operator on Hilbert space [H.sub.l] = [L.sup.2][(0, 1).sup.l] with Dirichlet-type boundary conditions.

If [alpha] [member of] N, the Caputo

differential operator coincides with the usual

differential operator of an integer order.

Note that,

differential operator equations were studied e.g.

In the framework of the drift-diffusion or density-gradient model F is a

differential operator, however, in the framework of the Boltzmann transport equation F becomes an integro-differential operator.

The

differential operator [[KAPPA].sup.n], n [member of] [N.sub.0] = N[union] {0}, is defined by Salagean [2] as follow: [mathematical expression not reproducible] (1.8)

Denotes the fractional

differential operator of order in the sense of Caputo.