Fernandez, ArranBaleanu, DumitruSrivastava, Hari M.02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2019-12-272025-09-182019-12-272025-09-182019Srivastava, Hari M.; Fernandez, Arran; Baleanu, Dumitru, "Some New Fractional-Calculus Connections between Mittag-Leffler Functions", Mathematics, Vol. 7, No. 6, (June 2019).2227-7390https://doi.org/10.3390/math7060485https://hdl.handle.net/123456789/11506Srivastava, Hari M./0000-0002-9277-8092; Fernandez, Arran/0000-0002-1491-1820We 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.eninfo:eu-repo/semantics/openAccessFractional IntegralsFractional DerivativesMittag-Leffler FunctionsArticle10.3390/math70604852-s2.0-85066855486