scholarly journals The two dimensional generalized Weyl fractional calculus and special functions

2010 ◽  
Vol 41 (2) ◽  
pp. 139-148
Author(s):  
V. B. L. Chaurasia ◽  
Mukesh Agnihotri
Keyword(s):  
Fractional Calculus ◽  
General Class ◽  
Special Functions ◽  
Fractional Integration ◽  
Two Dimensional ◽  
General Class Of Polynomials ◽  
Weyl Fractional Calculus

The object of this present paper is to derive a relation between the two dimensional I-transform involving a general class of polynomials and the Weyl type two dimensional Saigo operators of fractional integration. The results derived here are general in nature and include the results given earlier by Saigo, Saxena and Ram [10],Saxena and Ram [8], Saxena and Kiryakova [9] and Chaurasia and Srivastava [12].

scholarly journals Two-dimensional generalized Weyl fractional calculus pertaining to two-dimensional $ \overline{H} $-transforms

2006 ◽  
Vol 37 (3) ◽  
pp. 237-249
Author(s):  
V. B. L. Chaurasia ◽  
Amber Srivastava
Keyword(s):  
Fractional Calculus ◽  
Fractional Integration ◽  
Two Dimensional ◽  
Weyl Fractional Calculus

The aim of this paper is to establish a relation between the two-dimensional $ \overline{H} $-transform involving a general polynomials and the Weyl type two-dimensional Saigo operator of fractional integration.

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 A unified inverse Laplace transform formula involving the product of a general class of polynomials and the Fox $H$-function

2005 ◽  
Vol 36 (2) ◽  
pp. 87-92
Author(s):  
R. C. Soni ◽  
Deepika Singh
Keyword(s):  
Laplace Transform ◽  
General Class ◽  
Special Functions ◽  
Inverse Laplace Transform ◽  
General Class Of Polynomials ◽  
Special Cases ◽  
Main Formula

In the present paper we obtain the inverse Laplace transform of the product of a general class of polynomials and the Fox $H$-function. The polynomials and the functions involved in our main formula as well as their arguments are quite general in nature. Therefore, the inverse Laplace transform of the product of a large variety of polynomials and numerous simple special functions can be obtained as simple special cases of our main result. The results obtained by Gupta and Soni [2] and Srivastava [5] follow as special cases of our main result.

scholarly journals An Integral Involving Certain General Class of Polynomials and the Special Functions

2014 ◽  
Vol 10 (1) ◽  
pp. 07-13
Author(s):  
Ashok Singh Shekhawat ◽  
◽  
Parul Gupta ◽  
Rakeshwar Purohit
Keyword(s):  
General Class ◽  
Special Functions ◽  
General Class Of Polynomials

scholarly journals Fractional calculus pertaining to multivariable Aleph-function

2022 ◽  
Vol 40 ◽  
pp. 1-10
Author(s):  
Dinesh Kumar ◽  
Frederic Ayant
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
General Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
General Nature ◽  
Fractional Integral Operators ◽  
Mellin Transforms ◽  
General Class Of Polynomials

In this paper we study a pair of unied and extended fractional integral operator involving the multivariable Aleph-function, Aleph-function and general class of polynomials. During this study, we establish ve theorems pertaining to Mellin transforms of these operators. Furthers, some properties of these operators have also been investigated. On account of the general nature of the functions involved herein, a large number of (known and new) fractional integral operators involved simpler functions can also be obtained . We will quote the particular case concerning the multivariable I-function dened by Sharma and Ahmad [20] and the I-function of one variable dened by Saxena [13].

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