Srivastava, H.M.Fernandez, ArranBaleanu, Dumitru2019-07-222019-07-2220192019Srivastava, 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/math7060485http://dx.doi.org/10.3390/math7060485http://hdl.handle.net/1828/10983We 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.enfractional integralsfractional derivativesMittag–Leffler functionsArticle