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.

scholarly journals Pathway fractional integral operators of generalized k-wright function and k4-function

2017 ◽  
Vol 35 (2) ◽  
pp. 235 ◽  
Author(s):  
Dinesh Kumar ◽  
Ram Kishore Saxena ◽  
Jitendra Daiya
Keyword(s):  
Fractional Integral ◽  
Fractional Integration ◽  
Integral Operators ◽  
Wright Function ◽  
Finite Product ◽  
Fractional Integral Operators ◽  
Integral Formulas ◽  
Fractional Integration Operator ◽  
Composition Formula ◽  
Special Cases

In the present work we introduce a composition formula of the pathway fractional integration operator with finite product of generalized K-Wright function and K4-function. The obtained results are in terms of generalized Wright function.Certain special cases of the main results given here are also considered to correspond with some known and new (presumably) pathway fractional integral formulas.

scholarly journals Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
D. Baleanu ◽  
P. Agarwal ◽  
S. D. Purohit
Keyword(s):  
Bessel Function ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Integration ◽  
Fractional Integrals ◽  
General Character ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Generalized Bessel Functions ◽  
Special Cases

We apply generalized operators of fractional integration involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

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 Certain families of integral formulas involving Struve functions

2017 ◽  
Vol 37 (3) ◽  
pp. 27-35
Author(s):  
Junesang Choi ◽  
Nisar Koottakkaran Sooppy
Keyword(s):  
Bessel Functions ◽  
Wright Function ◽  
Hyperbolic Functions ◽  
Integral Formulas ◽  
Special Cases ◽  
Struve Functions

Recently, a large number of integral formulas involving Bessel functions and their extensions have been investigated. The objective of this paper is to establish four classes of integral formulas associated with the Struve functions, which are expressed in terms of the Fox-Wright function. Among a variety of special cases of the main results, we present only six integral formulas involving trigonometric and hyperbolic functions.

scholarly journals On Weyl fractional integral operators

2004 ◽  
Vol 35 (2) ◽  
pp. 169-174 ◽  
Author(s):  
Rashmi Jain ◽  
M. A. Pathan
Keyword(s):  
Hypergeometric Series ◽  
Fractional Integral ◽  
Integral Operators ◽  
Complex Numbers ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Arbitrary Complex ◽  
The Laplace Transform ◽  
Weyl Fractional Integral ◽  
Interesting Theorem

In this paper, we first establish an interesting theorem exhibiting a relationship existing between the Laplace transform and Weyl fractional integral operator of related functions. This theorem is sufficiently general in nature as it contains $n$ series involving arbitrary complex numbers $ \Omega(r_1,\ldots r_n) $. We have obtained here as applications of the theorem, the Weyl fractional integral operators of Kamp'e de F'eriet function, Appell's functions $ F_1 $, $ F_4 $, Humbert's function $ \Psi_1$ and Lauricella's, triple hypergeometric series $ F_E $. References of known results which follow as special cases of our theorem are also cited. Finally, we obtain some transformations of $ F^{(3)}$ and Kamp'e de F'eriet function with the application of our main theorem .

GENERALIZATION OF A RESULT INVOLVING PRODUCT OF GENERALIZED HYPERGEOMETRIC SERIES DUE TO RAMANUJAN

2013 ◽  
Vol 22 ◽  
pp. 679-685
Author(s):  
NIDHI SHEKHAWAT ◽  
OM PRAKASH
Keyword(s):  
Hypergeometric Series ◽  
Research Paper ◽  
Point Of View ◽  
Generalized Hypergeometric Series ◽  
Application Point ◽  
Special Cases ◽  
Summation Theorem

The aim of this research paper is to obtain a generalization of the following result involving product of generalized hypergeometric series due to Ramanujan. [Formula: see text]The results are derived with the help of generalized Kummer’s summation theorem, which recently added in the literature. A few very interesting contiguous results obtained earlier by Kim & Rathie follow special cases of our main findings. The results derived in this paper are simple, interesting, easily established and useful from application point of view.

Marichev-Saigo-Maeda fractional integral operators involving the product of generalized Bessel -Maitland functions

2021 ◽  
Vol 39 (1) ◽  
pp. 95-105
Author(s):  
D. L. Suthar ◽  
Praveen Agarwal ◽  
Hafte Amsalu
Keyword(s):  
Fractional Integral ◽  
Fractional Integration ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Fractional Integral Operators ◽  
Special Cases

The aim of this paper is to evaluate two theorems for fractional integration involving Appell’s function   due to Marichev-Saigo-Maeda, to the product of the generalized Bessel-Maitland function. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdẻlyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. Further, we point out also their relevance

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