Some New Fractional-Calculus Connections between Mittag–Leffler Functions
Date
2019
Authors
Srivastava, H.M.
Fernandez, Arran
Baleanu, Dumitru
Journal Title
Journal ISSN
Volume Title
Publisher
Mathematics
Abstract
We consider the well-known Mittag–Leffler functions of one, two and three parameters, and establish some new connections between them using fractional calculus. In particular, we express the three-parameter Mittag–Leffler function as a fractional derivative of the two-parameter Mittag–Leffler function, which is in turn a fractional integral of the one-parameter Mittag–Leffler function. Hence, we derive an integral expression for the three-parameter one in terms of the one-parameter one. We discuss the importance and applications of all three Mittag–Leffler functions, with a view to potential applications of our results in making certain types of experimental data much easier to analyse.
Description
Keywords
fractional integrals, fractional derivatives, Mittag–Leffler functions
Citation
Srivastava, H.M., Fernandez, A. & Baleanu, D. (2019). Some New Fractional- Calculus Connections between Mittag–Leffler Functions. Mathematics, 7(6), 485. https://doi.org/10.3390/math7060485