http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
A NEW EXTENSION OF THE MITTAG-LEFFLER FUNCTION
Arshad, Muhammad,Choi, Junesang,Mubeen, Shahid,Nisar, Kottakkaran Sooppy,Rahman, Gauhar Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.2
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.
Certain formulas involving a multi-index Mittag-Leffler function
P. Harjule,최준상,Manish Kumar Bansal,Shahid Mubeen,Devendra Kumar 영남수학회 2019 East Asian mathematical journal Vol.35 No.1
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 func- tion and, among possible numerous formulas, choose to present several for- mulas 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.
CERTAIN FORMULAS INVOLVING A MULTI-INDEX MITTAG-LEFFLER FUNCTION
Bansal, Manish Kumar,Harjule, P.,Choi, Junesang,Mubeen, Shahid,Kumar, Devendra The Youngnam Mathematical Society 2019 East Asian mathematical journal Vol.35 No.1
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.
NEW SEVEN-PARAMETER MITTAG-LEFFLER FUNCTION WITH CERTAIN ANALYTIC PROPERTIES
Maryam K. Rasheed,Abdulrahman H. Majeed 경남대학교 수학교육과 2024 Nonlinear Functional Analysis and Applications Vol.29 No.1
In this paper, a new seven-parameter Mittag-Leffler function of a single complex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and $H$-function is also developed.
THE EXTENDED k-MITTAG-LEFFLER FUNCTION AND ITS PROPERTIES
G. Rahman,K.S. NISAR,김태균,S. MUBEEN,M. ARSHAD 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.3
In this present paper, our aim is to derive the extended k- Mittag-Leffler function by using the extended k-beta function (Mubeen et al. in J. math. anal. Volume 7 Issue 5(2016), 118-131.) and de- ne some integral representation this newly dened function. Also, we introduce the extended k-fractional derivative formula and show that the extended k-fractional derivative k-fractional of the k-Mittag-Leffler gives the extended k-Mittag-Leffler function.
V. Padmapriya,M. Kaliyappan 한국지능시스템학회 2022 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.22 No.2
The matrix Mittag-Leffler functions play a crucial role in several applications related to systems with fractional dynamics. These functions represent a generalization for fractional-ordersystems of the matrix exponential function involved in integer-order systems. Computationaltechniques for evaluating the matrix Mittag-Leffler functions are therefore of particular importance. In this study, a fuzzy system of differential equations with fractional derivatives wassolved in terms of the matrix Mittag-Leffler functions. The matrix Mittag-Leffler function wasevaluated based on the Jordan canonical form and the minimal polynomial of the matrix
Mittag-Leffler stability of systems of fractional nabla difference equations
Paul Eloe,Jaganmohan Jonnalagadda 대한수학회 2019 대한수학회보 Vol.56 No.4
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.
Saliu Afis,Kanwal Jabeen,Semiu Oladipupo Oladejo,Olaide Yetunde Saka-Balogun 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.5
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.
MITTAG-LEFFLER STABILITY OF SYSTEMS OF FRACTIONAL NABLA DIFFERENCE EQUATIONS
Eloe, Paul,Jonnalagadda, Jaganmohan Korean Mathematical Society 2019 대한수학회보 Vol.56 No.4
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.
RADII PROBLEMS FOR THE GENERALIZED MITTAG-LEFFLER FUNCTIONS
Prajapati, Anuja Korean Mathematical Society 2020 대한수학회지 Vol.57 No.4
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.