In mathematics, the fractional Laplacian is an operator, which generalizes the notion of Laplacian spatial derivatives to fractional powers. This operator is often used to generalise certain types of Partial differential equation, two examples are [1] and [2] which both take known PDEs containing the Laplacian and replacing it with the fractional version.
^Melcher, Christof; Sakellaris, Zisis N. (2019-05-04). "Global dissipative half-harmonic flows into spheres: small data in critical Sobolev spaces". Communications in Partial Differential Equations. 44 (5): 397–415. arXiv:1806.06818. doi:10.1080/03605302.2018.1554675. ISSN 0360-5302.
^Wettstein, Jerome D. (2023). "Half-harmonic gradient flow: aspects of a non-local geometric PDE". Mathematics in Engineering. 5 (3): 1–38. arXiv:2112.08846. doi:10.3934/mine.2023058. ISSN 2640-3501.
and 26 Related for: Fractional Laplacian information
In mathematics, the fractionalLaplacian 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 fractionalLaplacian wave equation. See for a paper which compares fractional wave equations...
{\displaystyle y} . An example of a singular integral operator is the fractionalLaplacian ( − Δ ) s f ( x ) = c d , s ∫ R d f ( x ) − f ( y ) | x − y | d +...
In probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical...
mathematical analysis, initialization of the differintegrals is a topic in fractional calculus. The composition law of the differintegral operator states that...
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,...
In fractional calculus, an area of mathematical analysis, the differintegral is a combined differentiation/integration operator. Applied to a function...
test.) Another common generalization of the second derivative is the Laplacian. This is the differential operator ∇ 2 {\displaystyle \nabla ^{2}} (or...
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...
Differential Integral Series Vector Multivariable Advanced Specialized Fractional Malliavin Stochastic Variations Miscellaneous Precalculus History Glossary...
processing operators in image processing and computer vision (see the Laplacian of Gaussian (LoG) blob detector, the determinant of Hessian (DoH) blob...
formula describes the spectrum of differential operators such as the Laplacian in terms of geometric data involving the lengths of geodesics on the Riemann...
Differential Integral Series Vector Multivariable Advanced Specialized Fractional Malliavin Stochastic Variations Miscellaneous Precalculus History Glossary...
Differential Integral Series Vector Multivariable Advanced Specialized Fractional Malliavin Stochastic Variations Miscellaneous Precalculus History Glossary...
Differential Integral Series Vector Multivariable Advanced Specialized Fractional Malliavin Stochastic Variations Miscellaneous Precalculus History Glossary...
Differential Integral Series Vector Multivariable Advanced Specialized Fractional Malliavin Stochastic Variations Miscellaneous Precalculus History Glossary...
Differential Integral Series Vector Multivariable Advanced Specialized Fractional Malliavin Stochastic Variations Miscellaneous Precalculus History Glossary...
Differential Integral Series Vector Multivariable Advanced Specialized Fractional Malliavin Stochastic Variations Miscellaneous Precalculus History Glossary...
Differential Integral Series Vector Multivariable Advanced Specialized Fractional Malliavin Stochastic Variations Miscellaneous Precalculus History Glossary...
Global Information