scholarly journals Generalized Fractional Calculus Operators Associated with K-function

2020 ◽  
Vol 1 (2) ◽  
Author(s):  
D.L. Suthar
Keyword(s):  
Special Functions ◽  
General Nature ◽  
Fractional Integral Operators ◽  
Generalized Fractional Calculus ◽  
Fractional Calculus Operators ◽  
Generalized Fractional Integral ◽  
K Function ◽  
Generalized Fractional Calculus Operators ◽  
Fox’S H Function ◽  
Generalized Fractional Integral Operators

The aim of this paper is to study some properties of K-function introduced by Sharma. Here we establish two theorems which give the image of this K-function under the generalized fractional integral operators involving Fox’s H-function as kernel. Corresponding assertions in term of Euler, Whittaker and K-transforms are also presented. On account of general nature of H-function and K-function a number of results involving special functions can be obtained merely by giving particular values for the parameters.

scholarly journals A Study on Generalized Multivariable Mittag-Leffler Function via Generalized Fractional Calculus Operators

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
D. L. Suthar ◽  
Mitku Andualem ◽  
Belete Debalkie
Keyword(s):  
Integral Operators ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
Generalized Fractional Calculus ◽  
Special Cases ◽  
Fractional Calculus Operators ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Calculus Operators ◽  
Fox’S H Function ◽  
Generalized Fractional Integral Operators

We study some properties of generalized multivariable Mittag-Leffler function. Also we establish two theorems, which give the images of this function under the generalized fractional integral operators involving Fox’s H-function as kernel. Relating affirmations in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some known special cases have also been mentioned in the concluding section.

scholarly journals Generalized Fractional Integral Operators Involving Mittag-Leffler Function

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Hafte Amsalu ◽  
D. L. Suthar
Keyword(s):  
Fractional Integral ◽  
Special Functions ◽  
Integral Operators ◽  
General Nature ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

The aim of this paper is to study various properties of Mittag-Leffler (M-L) function. Here we establish two theorems which give the image of this M-L function under the generalized fractional integral operators involving Fox’s H-function as kernel. Corresponding assertions in terms of Euler, Mellin, Laplace, Whittaker, and K-transforms are also presented. On account of general nature of M-L function a number of results involving special functions can be obtained merely by giving particular values for the parameters.

scholarly journals Certain Properties of Generalized M-Series under Generalized Fractional Integral Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
D. L. Suthar ◽  
Fasil Gidaf ◽  
Mitku Andualem
Keyword(s):  
Laplace Transform ◽  
Fractional Integral ◽  
Special Functions ◽  
Integral Operators ◽  
General Nature ◽  
Transform Methods ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

The aim of this study is to introduce new (presumed) generalized fractional integral operators involving I -function as a kernel. In addition, two theorems have been developed under these operators that provide an image formula for this generalized M -series and also to study the different properties of the generalized M -series. The corresponding assertions in terms of Euler and Laplace transform methods are presented. Due to the general nature of the I -function and the generalized M -series, a number of results involving special functions can be achieved only by making appropriate values for the parameters.

scholarly journals On Generalized Fractional Integral Operators and the Generalized Gauss Hypergeometric Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Dumitru Baleanu ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Integral Transform ◽  
Special Functions ◽  
Fractional Integration ◽  
Fractional Integral Operators ◽  
Integral Formulas ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

A remarkably large number of fractional integral formulas involving the number of special functions, have been investigated by many authors. Very recently, Agarwal (National Academy Science Letters) gave some integral transform and fractional integral formulas involving theFpα,β·. In this sequel, here, we aim to establish some image formulas by applying generalized operators of the fractional integration involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda. Some interesting special cases of our main results are also considered.

scholarly journals Fractional Integration of the Product of two Multivariable Gimel-Functions and a General Class of Polynomials

2018 ◽  
pp. 33-48
Author(s):  
Frederic Ayant
Keyword(s):  
Fractional Calculus ◽  
General Class ◽  
Special Functions ◽  
Fractional Integration ◽  
General Nature ◽  
Fractional Integral Operators ◽  
Summation Of Series ◽  
Fractional Calculus Operators ◽  
The Subject ◽  
Interesting Account

A significantly large number of earlier works on the subject of fractional calculus give the interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, the summation of series, etc.). The object of the present paper is to study and develop the Saigo-Maeda operators. First, we establish four results that give the images of the product of two multivariable Gimel-functions and a general class of multivariable polynomials in Saigo- Maeda operators. On account of the general nature of the Saigo-Maeda operators, multivariable Gimel-functions and a class multivariable polynomials a large number of new and known theorems involving Riemann-Liouville and Erdelyi- Kober fractional integral operators and several special functions.

scholarly journals On Extended General Mittag–Leffler Functions and Certain Inequalities

2019 ◽  
Vol 3 (2) ◽  
pp. 32
Author(s):  
Marcela V. Mihai ◽  
Muhammad Uzair Awan ◽  
Muhammad Aslam Noor ◽  
Tingsong Du ◽  
Artion Kashuri ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Function Of Two Variables ◽  
Generalized Fractional Integral Operators

In this paper, we introduce and investigate generalized fractional integral operators containing the new generalized Mittag–Leffler function of two variables. We establish several new refinements of Hermite–Hadamard-like inequalities via co-ordinated convex functions.

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