On a generalization of Mittag-Leffler function and its properties

By A. Shukla, J. Prajapati. 2007

415 citations recorded by the source corpus.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/8a2e051e73dbfe988a11b703682378dae92efa71

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In Applied Mathematics

In Atomic and Molecular Physics, and Optics

In Modeling and Simulation

Citations in the corpus

Multivariate analogue of generalized Mittag-Leffler function (2011, background): “[34] A.K. Shukla, and J.C. Prajapati, On a generalization of Mittag-Leffler function and its properties, J. Math.”
A study of fractional integral operators involving a certain generalized multi‐index Mittag‐Leffler function (2018, background): “which exhibits the fact that not only the generalized multi-index Mittag-Leffler function Eγ,κ [ (αj, βj)j=1; z ] defined by (8), but indeed also all of the above-mentioned Mittag-Leffler–type functions and many more, are contained, as special cases, in the the extensively and widely investigated Fo”
A Mittag-Leffler-type function of two variables (2013, neutral): “[8] Shukla AK, Prajapati JC.”
Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments (2020, background): “A special case of the generalized Mittag-Leffler function E α,β (z) when κ = q ∈ (0, 1) ∪ N was studied earlier by Shukla and Prajapati (see [81]).”
Some Applications of Mittag-Leffler Function in the Unit Disk (2016, neutral): “in [1], [2], [3], [4], [5], [7], [12], [13],[14], [15], [16], [19], [20] and [21].”
The Role of the Mittag-Leffler Function in Fractional Modeling (2015, methodology): “Γ(αn+ β) (15) A generalization of Prabhakar function Equation (9) was given by Shukla and Prajapati [37]: Eγ,κα,β(z) := ∞∑ n=0 (γ)κnz n n!”
Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel (2009, background): “Compositional properties of the integral operator involving the generalized Mittag–Leffler function E a;bðzÞ with different indices In this section, we first present a generalization of the following known identity (see, for details, [12,20]): Z x”
The extended Mittag-Leffler function via fractional calculus (2017, background): “These results are the extended form of Mittag-Leffler function defined in ([39, 45]).”
On Ostrowski type inequalities (2016, background): “By choosing parameters suitably in (51) and (52), many important fractional integral operators including those involving the generalized Mittag-Leffler function as kernel (see [15], [16] and [18]) can be easily obtained and corresponding to these integral operators related inequalities from the Coro”