文章基本信息

标题：Fractional derivatives of the generalized Mittag-Leffler functions
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作者：Denghao Pang ; Wei Jiang ; Azmat U. K. Niazi 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2018
卷号：2018
期号：1
页码：415
DOI：10.1186/s13662-018-1855-9
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we derive the compositions of the fractional derivatives with the Shukla function, a four-parameter Mittag-Leffler function. We investigate and compare the difference between the Riemann–Liouville and Caputo derivatives of the generalized Mittag-Leffler functions and obtain the reason causing the difference and expand the fractional derivatives of the generalized Mittag-Leffler functions. Two illustrative examples and the related numerical results are provided to demonstrate the validity.
关键词：Mittag-Leffler function ; Riemann–Liouville derivative ; Caputo derivative