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Fractional generalization of Kac integral

✍ Scribed by Vasily E. Tarasov; George M. Zaslavsky

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
200 KB
Volume
13
Category
Article
ISSN
1007-5704

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✦ Synopsis

Generalization of the Kac integral and Kac method for paths measure based on the Le ´vy distribution has been used to derive fractional diffusion equation. Application to nonlinear fractional Ginzburg-Landau equation is discussed.

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## Abstract Let __L__ be the infinitesimal generator of an analytic semigroup on __L__^2^(ℝ^__n__^ ) with Gaussian kernel bound, and let __L__^–__α__ /2^ be the fractional integral of __L__ for 0 < __α__ < __n__. Suppose that __b__ = (__b__~1~, __b__~2~, …, __b__~__m__~ ) is a finite family of loca