Search results

In mathematics, the fractional Laplacian is an operator, which generalizes the notion of Laplacian spatial derivatives to fractional powers. This operator...

Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number...

In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean...

positive fractional derivative modified Szabo's wave equation and the fractional Laplacian wave equation. See for a paper which compares fractional wave equations...

In probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical...

{\displaystyle y} . An example of a singular integral operator is the fractional Laplacian ( − Δ ) s f ( x ) = c d , s ∫ R d f ( x ) − f ( y ) | x − y | d +...

mathematical analysis, initialization of the differintegrals is a topic in fractional calculus. The composition law of the differintegral operator states that...

In fractional calculus, an area of mathematical analysis, the differintegral is a combined differentiation/integration operator. Applied to a function...

z^{2}}}.} The Laplacian is a measure of how much a function is changing over a small sphere centered at the point. When the Laplacian is equal to 0,...

Liouville, the latter of whom was the first to consider the possibility of fractional calculus in 1832. The operator agrees with the Euler transform, after...

A fractional-order integrator or just simply fractional integrator is an integrator device that calculates the fractional-order integral or derivative...

test.) Another common generalization of the second derivative is the Laplacian. This is the differential operator ∇ 2 {\displaystyle \nabla ^{2}} (or...

QY., Ma, ZM. Reflected Symmetric α-Stable Processes and Regional Fractional Laplacian. Probab. Theory Relat. Fields 134, 649–694 (2006). https://doi.org/10...

\right)\cdot d\mathbf {S} .} In particular, this demonstrates that the Laplacian is a self-adjoint operator in the L2 inner product for functions vanishing...

allow for fractional calculus. Some of these operators are so important that they have their own names: The Laplace operator or Laplacian on R3 is a...

V'\right)\right]\end{aligned}}} where we have used the definition of the vector Laplacian: ∇ 2 a = ∇ ( ∇ ⋅ a ) − ∇ × ( ∇ × a )   , {\displaystyle \nabla ^{2}\mathbf...

Gradient Divergence Curl Laplacian Directional derivative Identities Theorems Gradient Green's Stokes' Divergence generalized Stokes Helmholtz decomposition...

z}}\right)\cdot \mathbf {A} \\&=\nabla \cdot \mathbf {A} \end{aligned}}} ∇2φ Laplacian: The Laplacian div ⁡ grad ⁡ φ {\displaystyle \operatorname {div} \operatorname...

processing operators in image processing and computer vision (see the Laplacian of Gaussian (LoG) blob detector, the determinant of Hessian (DoH) blob...

Differential Integral Series Vector Multivariable Advanced Specialized Fractional Malliavin Stochastic Variations Miscellaneous Precalculus History Glossary...