scholarly journals Some integral transforms of the generalized k-Mittag-Leffler function

2019 ◽  
Vol 106 (120) ◽  
pp. 125-133
Author(s):  
Feng Qi ◽  
Kottakkaran Nisar
Keyword(s):  
Integral Transforms ◽  
Wright Function ◽  
Generalized Wright Function

We generalize the notion ?k-Mittag-Leffler function?, establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

INTEGRAL TRANSFORM OF K4-FUNCTION

2021 ◽  
Vol 21 (2) ◽  
pp. 429-436
Author(s):  
SEEMA KABRA ◽  
HARISH NAGAR
Keyword(s):  
Laplace Transform ◽  
Hypergeometric Function ◽  
Integral Transform ◽  
Integral Transforms ◽  
Gauss Hypergeometric Function ◽  
Wright Function ◽  
Generalized Wright Function ◽  
Special Cases ◽  
Euler Transform

In this present work we derived integral transforms such as Euler transform, Laplace transform, and Whittaker transform of K4-function. The results are given in generalized Wright function. Some special cases of the main result are also presented here with new and interesting results. We further extended integral transforms derived here in terms of Gauss Hypergeometric function.

scholarly journals Some Integral Transforms of the Generalized k-Mittag-Leffler Function

2016 ◽  
Author(s):  
Feng Qi ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Integral Transforms ◽  
Wright Function ◽  
Generalized Wright Function

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

scholarly journals Computation of certain integral formulas involving generalized Wright function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Nabiullah Khan ◽  
Talha Usman ◽  
Mohd Aman ◽  
Shrideh Al-Omari ◽  
Serkan Araci
Keyword(s):  
Hypergeometric Function ◽  
Special Functions ◽  
Gaussian Quadrature ◽  
Integral Transforms ◽  
Wright Function ◽  
Gaussian Quadrature Formula ◽  
Integral Formulas ◽  
Generalized Wright Function ◽  
Special Cases ◽  
Generalized Wright Hypergeometric Function

Abstract The aim of the paper is to derive certain formulas involving integral transforms and a family of generalized Wright functions, expressed in terms of the generalized Wright hypergeometric function and in terms of the generalized hypergeometric function as well. Based on the main results, some integral formulas involving different special functions connected with the generalized Wright function are explicitly established as special cases for different values of the parameters. Moreover, a Gaussian quadrature formula has been used to compute the integrals and compare with the main results by using graphical representations.

scholarly journals Some Fractional Calculus Results Pertaining To Mittag-Leffler Type Functions

2017 ◽  
Vol 13 (1) ◽  
pp. 31-48
Author(s):  
Anupama Choudhary ◽  
Devendra Kumar ◽  
Jagdev Singh
Keyword(s):  
Fractional Calculus ◽  
Wright Function ◽  
Fractional Operators ◽  
Multi Index ◽  
Generalized Wright Function ◽  
Engineering And Technology

Abstract In this paper, we study the generalized fractional operators pertaining to the generalized Mittag-Leffler function and multi-index Mittag-Leffler function. Some applications of the established results associated with generalized Wright function are also deduced as corollaries. The results are useful in solving the problems of science, engineering and technology where the Mittag-Leffler function occurs naturally.

scholarly journals Certain integral Transforms of the generalized Lommel-Wright function

Cubo (Temuco) ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 49-60 ◽  
Author(s):  
S. Haq ◽  
K.S. Nisar ◽  
A.H. Khan ◽  
D.L. Suthar
Keyword(s):  
Integral Transforms ◽  
Wright Function

scholarly journals ON A NEW GENERALIZED BETA FUNCTION DEFINED BY THE GENERALIZED WRIGHT FUNCTION AND ITS APPLICATIONS

2021 ◽  
Vol 6 (2) ◽  
pp. 852
Author(s):  
UMAR MUHAMMAD ABUBAKAR ◽  
Soraj Patel
Keyword(s):  
Hypergeometric Functions ◽  
Special Functions ◽  
Beta Function ◽  
Integral Representations ◽  
Wright Function ◽  
Confluent Hypergeometric Functions ◽  
Summation Formulas ◽  
Generalized Wright Function ◽  
Beta Error ◽  
Extended Beta Function

Various extensions of classical gamma, beta, Gauss hypergeometric and confluent hypergeometric functions have been proposed recently by many researchers. In this paper, we further generalized extended beta function with some of its properties such as symmetric properties, summation formulas, integral representations, connection with some other special functions such as classical beta, error, Mittag – Leffler, incomplete gamma, hypergeometric, classical Wright, Fox – Wright, Fox H and Meijer G – functions. Furthermore, the generalized beta function is used to generalize classical and other extended Gauss hypergeometric, confluent hypergeometric, Appell’s and Lauricella’s functions.

scholarly journals Marichev-Saigo-Maeda Fractional Integration Operators Involving Generalized Bessel Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Saiful R. Mondal ◽  
K. S. Nisar
Keyword(s):  
Hypergeometric Series ◽  
Bessel Functions ◽  
Fractional Integration ◽  
Integral Operators ◽  
Sine Function ◽  
Wright Function ◽  
Generalized Hypergeometric Series ◽  
Generalized Wright Function ◽  
Generalized Bessel Functions ◽  
Special Cases

Two integral operators involving Appell's functions, or Horn's function in the kernel are considered. Composition of such functions with generalized Bessel functions of the first kind is expressed in terms of generalized Wright function and generalized hypergeometric series. Many special cases, including cosine and sine function, are also discussed.

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