The extended Mittag-Leffler function and its properties

DOI10.1186/1029-242X-2014-85zbMath1309.33021WikidataQ59318469 ScholiaQ59318469MaRDI QIDQ2258741

Banu Yılmaz, Mehmet Ali Özarslan

Publication date: 26 February 2015

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

zbMATH Keywords

Mellin transformLaguerre polynomialsfractional derivativeWhittaker functionsMittag-Lefflerextended beta functionsWright generalized hypergeometric functions

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Mittag-Leffler functions and generalizations (33E12)

Related Items (28)

Integral transforms of an extended generalized multi-index Bessel function ⋮ Extended Bessel-Maitland function and its properties pertaining to integral transforms and fractional calculus ⋮ The composition of extended Mittag-Leffler functions with pathway integral operator ⋮ Some results on the extended beta and extended hypergeometric functions ⋮ A basic study of a fractional integral operator with extended Mittag-Leffler kernel ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Pathway fractional integral formula involving an extended Mittag-Leffler function ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Certain integrals involving generalized Mittag-Leffler functions ⋮ Fractional integral operators involving extended Mittag-Leffler function as its kernel ⋮ The extended Bessel-Maitland function and integral operators associated with fractional calculus ⋮ A class of extended Mittag-Leffler functions and their properties related to integral transforms and fractional calculus ⋮ Unnamed Item ⋮ Fractional differential equations for the generalized Mittag-Leffler function ⋮ Unnamed Item ⋮ Extension of the fractional derivative operator of the Riemann-Liouville ⋮ The extended Mittag-Leffler function via fractional calculus ⋮ Unnamed Item ⋮ Beta operator with Caputo Marichev-Saigo-Maeda fractional differential operator of extended Mittag-Leffler function ⋮ An integral operator involving generalized Mittag-Leffler function and associated fractional calculus results ⋮ Laplace operator with Caputo-type Marichev-Saigo-Maeda fractional differential operator of extended Mittag-Leffler function ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Fractional calculus operators with Appell function kernels applied to Srivastava polynomials and extended Mittag-Leffler function ⋮ A new extension of the Pochhammer symbol and its application to hypergeometric functions

Cites Work

• On the generalized Mittag-Leffler function and its application in a fractional telegraph equation
• Mittag-Leffler functions and their applications
• Some generating relations for extended hypergeometric functions via generalized fractional derivative operator
• Extended hypergeometric and confluent hypergeometric functions

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