Certain Integral Transforms of Generalized k-Bessel Function

Journal of Mathematics

The main motive of this study is to present a new class of a generalized k -Bessel–Maitland function by utilizing the k -gamma function and Pochhammer k -symbol. By this approach, we deduce a few analytical properties as usual differentiations and integral transforms (likewise, Laplace transform, Whittaker transform, beta transform, and so forth) for our presented k -Bessel–Maitland function. Also, the k -fractional integration and k -fractional differentiation of abovementioned k -Bessel–Maitland functions are also pointed out systematically.

Bulletin of the Korean Mathematical Society, 2014

A remarkably large number of integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas involving various Bessel functions have been presented. Very recently, Choi and Agarwal derived two generalized integral formulas associated with the Bessel function Jν (z) of the first kind, which are expressed in terms of the generalized (Wright) hypergeometric functions. In the present sequel to Choi and Agarwal's work, here, in this paper, we establish two new integral formulas involving the generalized Bessel functions, which are also expressed in terms of the generalized (Wright) hypergeometric functions. 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.

Journal of Mathematics

The aim of this paper is to deal with two integral transforms involving the Appell function as their kernels. We prove some compositions formulas for generalized fractional integrals with k-Bessel function. The results are expressed in terms of generalized Wright type hypergeometric function and generalized hypergeometric series. Also, the authors presented some related assertion for Saigo, Riemann-Liouville type, and Erdélyi-Kober type fractional integral transforms.

Journal of Mathematical Analysis and Applications, 2005

A first kind Fredholm integral equation with nondegenerate kernel is given, which particular solution is the Bessel function of the first kind. This equation is solved by means of Mellin transform pair.

In this paper we introduce some special type of integral representation of Bessel function of first kind and give some nonstandard results applying on parameters p, n and variables x, t ,í µí»‰ for different nonstandard values (infinitesimals, infinitely close, unlimited,…).

Communications in Numerical Analysis, 2014

In recent years, several integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas containing the Bessel function J ν (z) have been presented. Very recently, Rakha et al. presented some generalized integral formulas involving the hypergeometric functions. In this sequel, here, we aim at establishing two generalized integral formulas involving a Bessel functions of the first kind, which are expressed in terms of the generalized Wright hypergeometric function. Some interesting special cases of our main results are also considered.

Arxiv preprint math/9307213, 1993

A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of products of three Bessel functions.

Computers & Mathematics with Applications, 1995

Bessel functions have been generalized in a number of ways and many of these generalizations have been proved to be important tools in applications. In this paper we present a unified treatment, thus proving that many of the seemingly different generalizations may be viewed as particular cases of a two-variable function of the type introduced by Miller during the sixties.

Applied Mathematics Letters, 2013

We use the operator method to evaluate a class of integrals involving Bessel or Besseltype functions. The technique we propose is based on the formal reduction of these family of functions to Gaussians.

Using a generalized form of confluent hypergeometric function [N.Virchenko: On a generalized confluent hypergeometric function and its generalizations. Fract. Calc.Appl. Anal. 9(2006), 101-108], we introduce some new integral transforms and obtain their inversion theorems. Parseval-Goldstein type relations are established. Classical integral transforms, such as Laplace, Stieltjes .Widder-Potential follow as special cases of general transforms considered here. Some examples are given.

Kyungpook Math. J., 2016

The main object of this paper is to present two general integral formulas whose integrands are the integrand given in the integral formula (3) and a finite product of the generalized Bessel function of the first kind.

Applied Mathematical Sciences, 2014

This paper is devoted to study integral transforms of extended version of generalized Mittag-Leffler function introduced by Prajapati et al [9].

2016

Abstract. The table of Gradshteyn and Ryzhik contains many integrals that can be evaluated using the modified Bessel function. Some examples are discussed and typos in the table are corrected. 1.

Mathematica Bohemica, 2016

We introduce and study some new subclasses of starlike, convex and closeto-convex functions defined by the generalized Bessel operator. Inclusion relations are established and integral operator in these subclasses is discussed.

Applications and Applied Mathematics: An International Journal (AAM), 2021

In the recent years, various generalizations of Bessel function were introduced and its various properties were investigated by many authors. Bessel-Maitland function is one of the generalizations of Bessel function. The objective of this paper is to establish a new generalization of Bessel-Maitland function using the extension of beta function involving Appell series and Lauricella functions. Some of its properties including recurrence relation, integral representation and differentiation formula are investigated. Moreover, some properties of Riemann-Liouville fractional operator associated with the new generalization of Bessel-Maitland function are also discussed.