Multidimensional modified fractional calculus operators involving a general class of polynomials

1998 ◽  
Vol 108 (3) ◽  
pp. 273-282
Author(s):  
S. P. Goyal ◽  
Tariq O. Salim
Keyword(s):  
Fractional Calculus ◽  
General Class ◽  
General Class Of Polynomials ◽  
Fractional Calculus Operators

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].

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 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.

On some Hardy-type inequalities for fractional calculus operators

2017 ◽  
Vol 11 (2) ◽  
pp. 438-457 ◽  
Author(s):  
Sajid Iqbal ◽  
Josip Pečarić ◽  
Muhammad Samraiz ◽  
Zivorad Tomovski
Keyword(s):  
Fractional Calculus ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Fractional Calculus Operators

scholarly journals Certain Fractional Derivative Formulae Involving the Product of a General Class of Polynomials and the Multivariable Gimel-Function

2018 ◽  
pp. 1-13
Author(s):  
Frédéric Ayant
Keyword(s):  
Fractional Derivative ◽  
General Class ◽  
Leibniz Rule ◽  
General Character ◽  
General Class Of Polynomials

In the present paper, we obtain three unified fractional derivative formulae. The first involves the product of a general class of polynomials and the multivariable Gimel-function. The second involves the product of a general class of polynomials and two multivariable Gimel-functions and has been obtained with the help of the generalized Leibniz rule for fractional derivatives.The last fractional derivative formulae also involves the product of a general class of polynomials and the multivariable Gimel-function but it is obtained by the application of the first fractional derivative formulae twice and, it involve two independents variables instead of one.The polynomials and the functions involved in all our fractional derivative formulae as well as their arguments which are of the type The formulae are the very general character and thus making them useful in applications. In the end, we shall give a particular case.

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