On some applications of the space-time fractional derivative

Advances in Difference Equations

Wasan Ajeel Ahmood¹  Adem Klman² 

[1] Department of Mathematics, Universiti Putra Malaysia, Serdang, Malaysia;Institute for Mathematical Research, Department of Mathematics, Universiti Putra Malaysia, Serdang, Malaysia

关键词: fractional derivative;    evolution equations;    anomalous diffusion;   

DOI  :  10.1186/s13662-016-1015-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this work, we study and extend the one-dimensional fractional derivative to the multidimensional space-time fractional derivative, determine the exact solution via the Laplace transform, and develop mathematical foundations of the respective operators. The multidimensional space-time fractional derivative is developed to augment the equations. The results show that this method is effective, convenient, and easily executable. The main advantage of the proposed approach is that it is an accurate analytical method (the Laplace transform method) that can be implemented for both space and time discretizations of the fractional derivatives and allows us to present new solutions to problems by certain applications for solving space-time fractional derivatives.

【 授权许可】

CC BY