• 제목/요약/키워드: Mittag-Leffler function

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CERTAIN FORMULAS INVOLVING A MULTI-INDEX MITTAG-LEFFLER FUNCTION

  • Bansal, Manish Kumar;Harjule, P.;Choi, Junesang;Mubeen, Shahid;Kumar, Devendra
    • East Asian mathematical journal
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    • 제35권1호
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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.

A NEW EXTENSION OF THE MITTAG-LEFFLER FUNCTION

  • Arshad, Muhammad;Choi, Junesang;Mubeen, Shahid;Nisar, Kottakkaran Sooppy;Rahman, Gauhar
    • 대한수학회논문집
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    • 제33권2호
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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.

NEW SEVEN-PARAMETER MITTAG-LEFFLER FUNCTION WITH CERTAIN ANALYTIC PROPERTIES

  • Maryam K. Rasheed;Abdulrahman H. Majeed
    • Nonlinear Functional Analysis and Applications
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    • 제29권1호
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    • pp.99-111
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    • 2024
  • 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.

MITTAG-LEFFLER STABILITY OF SYSTEMS OF FRACTIONAL NABLA DIFFERENCE EQUATIONS

  • Eloe, Paul;Jonnalagadda, Jaganmohan
    • 대한수학회보
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    • 제56권4호
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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.

Some Generating Relations of Extended Mittag-Leffler Functions

  • Khan, Nabiullah;Ghayasuddin, Mohd;Shadab, Mohd
    • Kyungpook Mathematical Journal
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    • 제59권2호
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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.

SEVEN-PARAMETER MITTAG-LEFFLER OPERATOR WITH SECOND-ORDER DIFFERENTIAL SUBORDINATION RESULTS

  • Maryam K. Rasheed;Abdulrahman H. Majeed
    • Nonlinear Functional Analysis and Applications
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    • 제28권4호
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    • pp.903-917
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    • 2023
  • This paper constructs a new linear operator associated with a seven parameters Mittag-Leffler function using the convolution technique. In addition, it investigates some significant second-order differential subordination properties with considerable sandwich results concerning that operator.

ON GEOMETRIC PROPERTIES OF THE MITTAG-LEFFLER AND WRIGHT FUNCTIONS

  • Das, Sourav;Mehrez, Khaled
    • 대한수학회지
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    • 제58권4호
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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.

SOME INTEGRALS ASSOCIATED WITH MULTIINDEX MITTAG-LEFFLER FUNCTIONS

  • KHAN, N.U.;USMAN, T.;GHAYASUDDIN, M.
    • Journal of applied mathematics & informatics
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    • 제34권3_4호
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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.