A Project Report on Properties of the Mittag-Lefﬂer Functions and their Relations with Some Special Functions

Kassa, Adane

dc.contributor.author	Kassa, Adane
dc.date.accessioned	2020-09-08T06:58:35Z
dc.date.available	2020-09-08T06:58:35Z
dc.date.issued	2020-09-07
dc.identifier.uri	http://hdl.handle.net/123456789/11186
dc.description.abstract	Abstract Let g be a complex constant and z be complex variable, G(g) the Euler’s gamma function, and (g) k = G(g+k) G(g) for k 2 N[f0g the generalized Pochhammer symbol. The principal aim of this project is to investigate some properties of the Mittag-Lefﬂer function deﬁned by E g a;b (z) = ¥ å k=0 (g) G(ak +b) z k k k! ; where a; b; g 2 C and Â(a) > 0; Â(b) > 0; Â(g) > 0 and to study its relations with some other special functions of fractional calculus. The function E g a;b (z) is the generalization of the exponential function, the conﬂuent hypergeometric function, the classical wright function, the Mittag-Lefﬂer function of one and two parameters. For the function E g a;b (z), its various properties including Laplace transforms, Euler (Beta) transforms, Whittaker transforms, generalized hypergeometric series form, Mellin–Barnes integral representation with their some special cases are obtained. The usual differentiation and integration, fractional integration and differentiation of E (z) in Riemann-Liouville’s and Caputo’s senses are also obtained and relations with Conﬂuent hypergeometric function, Meijer’s G-function, Fox H-function and Wright hypergeometric functions are veriﬁed. g a;b	en_US
dc.language.iso	en_US	en_US
dc.subject	Mathematics	en_US
dc.title	A Project Report on Properties of the Mittag-Lefﬂer Functions and their Relations with Some Special Functions	en_US
dc.type	Thesis	en_US