Some New Extensions on Fractional Differential and Integral Properties for Mittag-Leffler Confluent Hypergeometric Function

Fractal and Fractional

卷:5

Hiba F. Al-Janaby¹  F. Ghanim²  Omar Bazighifan³ 

[1] Department of Mathematics, College of Sciences, University of Baghdad, Baghdad 10081, Iraq;

[2] Department of Mathematics, College of Sciences, University of Sharjah, Sharjah 27272, United Arab Emirates;

[3] Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy;

关键词: mittag-leffler function;    laplace transform;    confluent hypergeometric function;    fractional calculus;    integral operator;   

DOI  :  10.3390/fractalfract5040143

来源: DOAJ

【 摘 要 】

This article uses fractional calculus to create novel links between the well-known Mittag-Leffler functions of one, two, three, and four parameters. Hence, this paper studies several new analytical properties using fractional integration and differentiation for the Mittag-Leffler function formulated by confluent hypergeometric functions. We construct a four-parameter integral expression in terms of one-parameter. The paper explains the significance and applications of each of the four Mittag-Leffler functions, with the goal of using our findings to make analyzing specific kinds of experimental results considerably simpler.

【 授权许可】

Unknown