The Dirichlet problem for the time-fractional advection-diffusion equation in a line segment

Boundary value problems

Yuriy Povstenko¹  Joanna Klekot⁵ 

[1] Institute of Mathematics and Computer Science, Jan DłInstitute of Mathematics, Czȩstochowa University of Technology, Czȩstochowa, Poland;ugosz University, Czȩ

关键词: fractional calculus;    Caputo fractional derivative;    non-Fickian diffusion;    fractional advection-diffusion equation;    Mittag-Leffler function;    26A33;    45K05;   

DOI  :  10.1186/s13661-016-0597-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered in a line segment. The fundamental solution to the Dirichlet problem and the solution of the problem with a constant boundary condition are obtained using the integral transform technique. The numerical results are illustrated graphically.

【 授权许可】

CC BY