Fractional Fokker-Planck Equation

被引：8

作者：

Baumann, Gerd ^{[1
,2
]}

Stenger, Frank ^{[3
]}

机构：

[1] German Univ Cairo, Dept Math, New Cairo City 11835, Egypt

[2] Univ Ulm, D-89069 Ulm, Germany

[3] Univ Utah, Salt Lake City, UT 84112 USA

来源：

MATHEMATICS | 2017年 / 5卷 / 01期

关键词：

sinc methods; approximation; computation; integral equations; Riesz-Feller derivative; Caputo derivative; fractional Fokker Planck equation; DISCRETIZED OPERATIONAL CALCULUS; CONTINUOUS-TIME FINANCE; CONVOLUTION QUADRATURE; FUNDAMENTAL SOLUTION; SINC METHODS; DIFFUSION;

D O I：

10.3390/math5010012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We shall discuss the numerical solution of the Cauchy problem for the fully fractional Fokker-Planck (fFP) equation in connection with Sinc convolution methods. The numerical approximation is based on Caputo and Riesz-Feller fractional derivatives. The use of the transfer function in Laplace and Fourier spaces in connection with Sinc convolutions allow to find exponentially converging computing schemes. Examples using different initial conditions demonstrate the effective computations with a small number of grid points on an infinite spatial domain.

引用

页数：19

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