On a Unified Mittag-Leffler Function and Associated Fractional Integral Operator | Zendy

Yanyan Zhang | Zendy; Ghulam Farid | Zendy; Zabidin Salleh | Zendy; Ayyaz Ahmad | Zendy

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On a Unified Mittag-Leffler Function and Associated Fractional Integral Operator

Author(s) -

Yanyan Zhang,

Ghulam Farid,

Zabidin Salleh,

Ayyaz Ahmad

Publication year - 2021

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2021/6043769

Subject(s) - mittag leffler function , mathematics , fractional calculus , laplace transform , function (biology) , operator (biology) , euler's formula , beta function (physics) , exponential integral , green's function for the three variable laplace equation , pure mathematics , mathematical analysis , integral equation , inverse laplace transform , volume integral , physics , repressor , chemistry , quantum , biology , biochemistry , quantum mechanics , evolutionary biology , transcription factor , relationship between string theory and quantum field theory , quantum gravity , gene

The aim of this paper is to unify the extended Mittag-Leffler function and generalized Q function and define a unified Mittag-Leffler function. Both the extended Mittag-Leffler function and generalized Q function can be obtained from the unified Mittag-Leffler function. The Laplace, Euler beta, and Whittaker transformations are applied for this function, and generalized formulas are obtained. These formulas reproduce integral transformations of various deduced Mittag-Leffler functions and Q function. Also, the convergence of this unified Mittag-Leffler function is proved, and an associated fractional integral operator is constructed.

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