differential operator


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differential operator

n
(Mathematics) any operator involving differentiation, such as the mathematical operator del ∇, used in vector analysis, where ∇ = i∂/∂x + j∂/∂y+ k∂/∂z, i, j, and k being unit vectors and ∂/∂x, ∂/∂y, and ∂/∂z the partial derivatives of a function in x, y, and z
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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.

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