# differential operator

(redirected from Derivative operator)
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Related to Derivative operator: Integral operator, Linear differential operator

## 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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mathematical expression not reproducible] denotes Caputo's fractional derivative operator [11-13], [mathematical expression not reproducible], since Caputo's fractional derivative allows us to couple the fractional differential equations with initial conditions in the traditional form [mathematical expression not reproducible].
Baleanu and Mustafa present their own findings and some by others during the past few years into fractional calculus, which is used to study the fractional order integral and derivative operator over real and complex domains.
The Caputo definition of fractal derivative operator is given by
Indeed, many other methods like ADI-FDTD [18], LOD-FDTD [19], and CN FDTD [20] use the same discrete derivative operator as the S-FDTD method.
n-z)] and each side defines a different fractional derivative operator.
On Harmonic Functions Defined by Derivative Operator.
5, 6, 3]), Hohlov linear operator [7], the Carlson-Shaffer linear operator [2], the Ruscheweyh derivative operator [13], the generalized BernardiLibera-Livingston linear integral operator (cf.
The method consists of splitting the given equation into linear and non-linear parts, inverting the highest order derivative operator contained in the linear operator on both sides identifying the initial conditions and the terms involving the independent variables alone as initial approximation, decomposing the unknown function into a series whose components can be easily computed, decomposing the non-linear function in terms if polynomial called Adomian's polynomials, and finding the successive terms of the series solution by recurrent relation using the polynomials obtained (cf.
Direction of action of the derivative operator is not essential here, since the substitution [U.
The second vertical derivative operator has the effect of sharpening anomalies (Bakkali, 2006a).

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