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 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 Fractional calculus pertaining to multivariable I-function defined by Prathima

2019 ◽  
Vol 15 (2) ◽  
pp. 61-73
Author(s):  
D. Kumar ◽  
F. Y. Ayant
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
General Class ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
General Nature ◽  
Fractional Integral Operators ◽  
Mellin Transforms

Abstract In this paper, we study a pair of unified and extended fractional integral operator involving the multivariable I-functions and general class of multivariable polynomials. Here, we use Mellin transforms to obtain our main results. Certain properties of these operators concerning to their Mellin-transforms have been investigated. On account of the general nature of the functions involved herein, a large number of known (may be new also) fractional integral operators involved simpler functions can be obtained. We will also quote the particular case of the multivariable H-function.

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 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 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 AN ELEMENTARY AND INTRODUCTORY APPROACH TO FRACTIONAL CALCULUS AND ITS APPLICATIONS

2017 ◽  
Vol 29 (1-2) ◽  
Author(s):  
Hari M. Srivastava
Keyword(s):  
Fractional Calculus ◽  
Integral Equations ◽  
Special Functions ◽  
Mathematical Physics ◽  
Science And Engineering ◽  
The Past ◽  
Fractional Differintegral ◽  
The Subject ◽  
Derivatives Of ◽  
Differential And Integral Equations

A b s t r a c t: The subject of fractional calculus (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. It does indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this paper* is to present a brief elementary and introductory approach to the theory of fractional calculus and its applications especially in developing solutions of certain interesting families of ordinary and partial fractional differintegral equations. Relevant connections of some of the results presented in this lecture with those obtained in many other earlier works on this subject will also be indicated.

scholarly journals New fractional calculus results involving Srivastava’s general class of multivariable polynomials and The H̅ - function

2015 ◽  
Vol 11 (1) ◽  
pp. 19-32
Author(s):  
V. B. L. Chaurasia ◽  
Vinod Gill
Keyword(s):  
Differential Operator ◽  
Fractional Calculus ◽  
Wide Class ◽  
Mathematical Analysis ◽  
Fractional Differential Operator ◽  
Fractional Calculus Operators ◽  
Fractional Differential ◽  
Interesting Special Case ◽  
Special Case ◽  
Interesting Account

Abstract A significantly large number of earlier works on the subjects of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis. In the present paper, we study and develop an important result involving a fractional differential operator for the product of general multivariable polynomials, general polynomial set and two -functions. The result discussed here can be used to investigate a wide class of new and known results, hitherto scattered in the literature. For the sake of illustration, six interesting special case have also been recorded here of our main findings.

scholarly journals Fractional integration of certain special functions

2004 ◽  
Vol 35 (1) ◽  
pp. 13-22
Author(s):  
V. B. L. Chaurasia ◽  
Vijay Kumar Singhal
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Fractional Integral ◽  
Special Functions ◽  
Fractional Integration ◽  
Complex Variables ◽  
Fractional Integral Operator ◽  
Several Complex Variables ◽  
Generalized Polynomials

We derive an Eulerian integral and a main theorem based upon the fractional integral operator associated with generalized polynomials given by Srivastava [8. 185, Eq.~(7)] and $H$-function of several complex variables given by Srivastava and Panda [11, p.271, Eq.~(4.1)] which provide unification and extension of numerous results in the theory of fractional calculus of special functions in one and more variables. Certain interesting sepcial cases (known and new) have also been discussed.

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