The Extended Multi-Index Mittag-Leffler Functions and Their Properties Connected with Fractional Calculus and Integral Transforms

Praveen Agarwal; D. L. Suthar; Shilpi Jain; Shaher Momani

The Extended Multi-Index Mittag-Leffler Functions and Their Properties Connected with Fractional Calculus and Integral Transforms

Praveen Agarwal
, D. L. Suthar
, Shilpi Jain
, Shaher Momani

Nonlinear Dynamic Research Centre (NDRC)

International College of Engineering
Wollo University
Poornima College of Engineering
University of Jordan

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The aim of this paper is to present the extended multi-index Mittag-Leffler type functions while using the extended Beta function and investigate several properties including integral representation, Derivatives, Beta transform, Mellin transform, Relationships between this function with the Leguerre polynomials and Whittakar functions. Further, several properties of the Riemann-Liouville fractional derivative and integral operators related to extended multi-index Mittag-Leffler functions are also investigated. Finally, various interesting special cases of these functions are also pointed out.

Original language	English
Pages (from-to)	1251-1266
Number of pages	16
Journal	Thai Journal of Mathematics
Volume	20
Issue number	3
State	Published - Sep 2022

Keywords

Beta transform
Extended beta function
Extended multi-index Mittag-Leffler function
Laguerre polynomials
Mellin transform
Riemann-Liouville fractional calculus operators
Whittaker functions

Cite this

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title = "The Extended Multi-Index Mittag-Leffler Functions and Their Properties Connected with Fractional Calculus and Integral Transforms",

abstract = "The aim of this paper is to present the extended multi-index Mittag-Leffler type functions while using the extended Beta function and investigate several properties including integral representation, Derivatives, Beta transform, Mellin transform, Relationships between this function with the Leguerre polynomials and Whittakar functions. Further, several properties of the Riemann-Liouville fractional derivative and integral operators related to extended multi-index Mittag-Leffler functions are also investigated. Finally, various interesting special cases of these functions are also pointed out.",

keywords = "Beta transform, Extended beta function, Extended multi-index Mittag-Leffler function, Laguerre polynomials, Mellin transform, Riemann-Liouville fractional calculus operators, Whittaker functions",

author = "Praveen Agarwal and Suthar, \{D. L.\} and Shilpi Jain and Shaher Momani",

year = "2022",

month = sep,

language = "English",

volume = "20",

pages = "1251--1266",

journal = "Thai Journal of Mathematics",

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T1 - The Extended Multi-Index Mittag-Leffler Functions and Their Properties Connected with Fractional Calculus and Integral Transforms

AU - Agarwal, Praveen

AU - Suthar, D. L.

AU - Jain, Shilpi

AU - Momani, Shaher

PY - 2022/9

Y1 - 2022/9

N2 - The aim of this paper is to present the extended multi-index Mittag-Leffler type functions while using the extended Beta function and investigate several properties including integral representation, Derivatives, Beta transform, Mellin transform, Relationships between this function with the Leguerre polynomials and Whittakar functions. Further, several properties of the Riemann-Liouville fractional derivative and integral operators related to extended multi-index Mittag-Leffler functions are also investigated. Finally, various interesting special cases of these functions are also pointed out.

AB - The aim of this paper is to present the extended multi-index Mittag-Leffler type functions while using the extended Beta function and investigate several properties including integral representation, Derivatives, Beta transform, Mellin transform, Relationships between this function with the Leguerre polynomials and Whittakar functions. Further, several properties of the Riemann-Liouville fractional derivative and integral operators related to extended multi-index Mittag-Leffler functions are also investigated. Finally, various interesting special cases of these functions are also pointed out.

KW - Beta transform

KW - Extended beta function

KW - Extended multi-index Mittag-Leffler function

KW - Laguerre polynomials

KW - Mellin transform

KW - Riemann-Liouville fractional calculus operators

KW - Whittaker functions

UR - https://www.scopus.com/pages/publications/85139461567

M3 - Article

AN - SCOPUS:85139461567

SN - 1686-0209

VL - 20

SP - 1251

EP - 1266

JO - Thai Journal of Mathematics

JF - Thai Journal of Mathematics

IS - 3

ER -

The Extended Multi-Index Mittag-Leffler Functions and Their Properties Connected with Fractional Calculus and Integral Transforms

Abstract

Keywords

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