• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.325-333
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• 2019

Motivated by the results on generating functions investigated by H. Exton and many other authors, we derive certain (presumably) new generating functions for generalized Mittag-Leffler-type functions. Specifically, we introduce a new class of generating relations (which are partly bilateral and partly unilateral) involving the generalized Mittag-Leffler function. Also we present some special cases of our main result.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.977-992
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• 2019

Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.549-560
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• 2018

Since Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903, due to its usefulness and diverse applications, a variety and large number of its extensions (and generalizations) and variants have been presented and investigated. In this sequel, we aim to introduce a new extension of the Mittag-Leffler function by using a known extended beta function. Then we investigate ceratin useful properties and formulas associated with the extended Mittag-Leffler function such as integral representation, Mellin transform, recurrence relation, and derivative formulas. We also introduce an extended Riemann-Liouville fractional derivative to present a fractional derivative formula for a known extended Mittag-Leffler function, the result of which is expressed in terms of the new extended Mittag-Leffler functions.

• East Asian mathematical journal
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• v.35 no.1
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• pp.23-30
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• 2019

Since Mittag-Leffler introduced the so-called Mittag-Leffler function, a number of its extensions have been investigated due mainly to their applications in a variety of research subjects. Shukla and Prajapati presented a lot of formulas involving a generalized Mittag-Leffler function in a systematic manner. Motivated mainly by Shukla and Prajapati's work, we aim to investigate a generalized multi-index Mittag-Leffler function and, among possible numerous formulas, choose to present several formulas involving this generalized multi-index Mittag-Leffler function such as a recurrence formula, derivative formula, three integral transformation formulas. The results presented here, being general, are pointed out to reduce to yield relatively simple formulas including known ones.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.937-946
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• 2023

In this present work, we inaugurated subclasses of analytic functions which are associated with generalized Mittag Leffler Functions. Inclusion implications and integral preserving properties under the Bernardi integral operator are investigated. Some consequences of these findings are also illustrated.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.577-590
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• 2020

In this paper, new subclasses of analytic functions are proposed by using Mittag-Leffler function. Also some properties of these classes are studied in regard to coefficient inequality, distortion theorems, extreme points, radii of starlikeness and convexity and obtained numerous sharp results.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.1031-1052
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• 2020

In this paper our aim is to find various radii problems of the generalized Mittag-Leffler function for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions are analytic. The basic tool of this study is the Mittag-Leffler function in series. Also we have shown that the obtained radii are the smallest positive roots of some functional equations.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.249-255
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• 2016

The object of the present paper is to establish two interesting unified integral formulas involving Multiple (multiindex) Mittag-Leffler functions, which is expressed in terms of Wright hypergeometric function. Some deduction from these results are also considered.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.691-700
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• 2018

The main object of the present research paper is to establish two (potentially) useful Euler type integrals involving multiindex Mittag-Leffler functions, which are expressed in terms of Wright hypergeometric functions. Some deductions of the main results are also indicated.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.949-965
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• 2021

The main focus of the present paper is to present new set of sufficient conditions so that the normalized form of the Mittag-Leffler and Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit disk. Interesting consequences and examples are derived to support that these results are better than the existing ones and improve several results available in the literature.