• 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.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.851-856
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• 2013

The principal aim of this paper is to investigate a recurrence relation and an integral representation of k-Mittag-Leffler function introduced earlier by Dorrego and Cerutti [2] and several special cases have also been discussed.

• 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.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.417-423
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• 2019

In the paper, by virtue of the $Fa{\grave{a}}$ di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Mittag-Leffler polynomials.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.125-134
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• 2019

Since the Mittag-Leffler function was introduced in 1903, a variety of extensions and generalizations with diverse applications have been presented and investigated. In this paper, we aim to introduce some presumably new and remarkably different extensions of the Mittag-Leffler function, and use these to present the pathway fractional integral formulas. We point out relevant connections of some particular cases of our main results with known 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.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.203-211
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• 2019

In this note, new sharpened Redheffer type inequalities related to the Fox-Wright functions are established. As consequence, we show new Redheffer type inequalities for hypergeometric functions and for the four-parametric Mittag-Leffler functions with best possible exponents.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.461-468
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• 2023

This paper attempts to investigate a new subfamily 𝓢𝓣_𝜗,𝜎 (𝛼, 𝛽, 𝛾, 𝜇) of spirallike functions endowed with Mittag-Leffler and Wright functions. The paper further investigates sharp coefficient bounds for functions that belong to this class.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.749-763
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• 2021

This research article deals with the Mittag-Leffler-Hyers-Ulam stability of linear and impulsive fractional order differential equation which involves the Caputo derivative. The application of the generalized fractional Fourier transform method and fixed point theorem, evaluates the existence, uniqueness and stability of solution that are acquired for the proposed non-linear problems on Lizorkin space. Finally, examples are introduced to validate the outcomes of main result.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1115-1125
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• 2023

This paper deals with the controllability of linear and nonlinear generalized fractional dynamical systems in finite dimensional spaces. The results are obtained by using fractional calculus, Mittag-Leffler function and Schauder's fixed point theorem. Observability of linear system is also discussed. Examples are given to illustrate the theory.