Analytical solutions to multi-term time-space Caputo-Riesz fractional diffusion equations on an infinite domain

Advances in Difference Equations

Chung-Sik Sin¹  Mun-Chol Kim¹  Gang-Il Ri² 

[1] Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea

关键词: analytical solution;    Caputo fractional derivative;    Riesz fractional derivative;    multi-term fractional diffusion equation;    multivariate Mittag-Leffler function;    26A33;    35E15;    35K05;    35R11;    45K05;   

DOI  :  10.1186/s13662-017-1369-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The present paper deals with the Cauchy problem for the multi-term time-space fractional diffusion equation in one dimensional space. The time fractional derivatives are defined as Caputo fractional derivatives and the space fractional derivative is defined in the Riesz sense. Firstly the domain of the fractional Laplacian is extended to a Banach space. Then the analytical solutions are established by using the Luchko theorem and the multivariate Mittag-Leffler function.

【 授权许可】

CC BY