An Extension of the Mittag-Leffler Function and Its Associated Properties

Rahman, Gauhar; Saboor, Abdus; Anjum, Zunaira; Nisar, Kottakkaran Sooppy; Abdeljawad, Thabet

doi:10.1155/2020/5792853

Cited by 6 publications

(5 citation statements)

References 18 publications

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“…where q 0, α, β, x ∈ C; (α) > 0, (β) > 0, (p) > 0. Rahman et al [31], defined the following extension of Mittag Leffler functin by…”

Section: Modified Version Of MML Function and Its Special Casesmentioning

confidence: 99%

Exploring multi-index functions with significance relations and associated with general properties in fractional calculus

Ali,

Liaqat,

Tajer

et al. 2024

J. Math. Computer Sci.

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The extensions and generalization of the special functions including in particular Pochhammer symbol, hypergeometric functions, Mittag-Leffler type functions, and Bessel-Maitland functions are the main core for the development of fractional operators by means of its kernel. We present a new extension of the multi-inde Mittag Leffler (MML) function and multiindex Bessel-Maitland (MBM) function by using the generalized Pochhammer symbol. Moreover, we establish some significance relations of such type of multi-index functions with other existing versions of Mittag-Leffler and Bessel-Maitland functions. Moreover, we analyze the behavior of some well-known fractional operators like as Saigo's fractional integral (SFI), Erdeyli fractional integral (EFI) and Riemann fractional integral (RFI) with the product of newly describe multi-index functions.

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“…where q 0, α, β, x ∈ C; (α) > 0, (β) > 0, (p) > 0. Rahman et al [31], defined the following extension of Mittag Leffler functin by…”

Section: Modified Version Of MML Function and Its Special Casesmentioning

confidence: 99%

Exploring multi-index functions with significance relations and associated with general properties in fractional calculus

Ali,

Liaqat,

Tajer

et al. 2024

J. Math. Computer Sci.

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“…(2.60) Theorem 2. 10 The following recursion formulas hold true for the numerator parameters ρ 1 , ρ 2 , ρ 3 , ρ 4 of X (4) 98 :…”

Section: 30)mentioning

confidence: 99%

“…Many modern mathematics and theoretical physics problems lead to the study of the hypergeometric functions of several complex variables (see, e.g., [5][6][7][8][9][10][11][12][13][14][15][16]). These include, for example, problems in the representation theory, combinatorics, number theory, analytic continuation of integrals of the Mellin-Barnes type, and algebraic geometry.…”

Section: Introductionmentioning

confidence: 99%

Recursion formulas for certain quadruple hypergeometric functions

et al. 2021

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A remarkably large number of hypergeometric (and generalized) functions and a variety of their extensions have been presented and investigated in the literature by many authors. In this paper, we introduce five new hypergeometric functions in four variables and then establish several recursion formulas for these new functions. Some interesting particular cases and consequences of the main results are also considered.

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“…Definition 7. [29,30] The Mellin transform of integrable function ( ) with index is defined by * ( ) = { ( );…”

Section: Introductionmentioning

confidence: 99%

New extension of beta, Gauss and confluent hypergeometric functions

Abubakar

Kaurangini

2021

Cumhuriyet Science Journal

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There are many extensions and generalizations of Gamma and Beta functions in the literature. However, a new extension of the extended Beta function , 1 2 ; 1 , 2 ( 1 , 2 ) was introduced and presented here because of its important properties. The new extended Beta function has symmetric property, integral representations, Mellin transform, inverse Mellin transform and statistical properties like Beta distribution, mean, variance, moment and cumulative distribution which ware also presented. Finally, the new extended Gauss and Confluent Hypergeometric functions with their propertied were introduced and presented.

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An Extension of the Mittag-Leffler Function and Its Associated Properties

Cited by 6 publications

References 18 publications

Exploring multi-index functions with significance relations and associated with general properties in fractional calculus

Exploring multi-index functions with significance relations and associated with general properties in fractional calculus

Recursion formulas for certain quadruple hypergeometric functions

New extension of beta, Gauss and confluent hypergeometric functions

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