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Fractional Derivatives and Integrals on Time Scales via the Inverse Generalized Laplace Transform
fractional derivatives and integrals time scales Laplace transform
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2011/1/19
We introduce a fractional calculus on time scales using the theory of delta (or nabla)dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary ...
Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation
Dirichlet heat kernel fractional Laplacian gradient perturbation
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2010/11/19
Suppose $d\geq 2$ and $\alpha \in (1, 2)$. Let $D$ be a bounded $C^{1,1}$ open set in $R^d$ and $b$ an $R^d$-valued function on $R^d$ whose components are in a certain Kato class of the rotationally ...
Non-Local Tug-of-War and the Infinity Fractional Laplacian
Non-Local Tug-of-War the Infinity Fractional Laplacian
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2010/11/15
Motivated by the "tug-of-war" game studied in [12], we consider a "non-local" version of the game which goes as follows: at every step two players pick respectively a direction and then, instead of f...
On fractional parts of powers of real numbers close to 1
fractional parts of powers real numbers close to 1
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2010/12/10
We prove that there exist arbitrarily small positive real num-bers " such that every integral power (1 + ")n is at a distance greater than 2−17"| log "|−1 to the set of rational integers. ...