Fractional derivatives of the generalized Mittag-Leffler functions

Advances in Difference Equations

Wei Jiang¹  Denghao Pang¹  Azmat U. K. Niazi¹ 

[1] School of Mathematical Sciences, Anhui University;

关键词: Mittag-Leffler function;    Riemann–Liouville derivative;    Caputo derivative;   

DOI  :  10.1186/s13662-018-1855-9

来源: DOAJ

【 摘 要 】

Abstract 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.

【 授权许可】

Unknown