South East Asian J of Mathematics and Mathematical Sciences, Aug 29, 2023
The current study aims to describe the generalized Bessel function's pathway fractional integral ... more The current study aims to describe the generalized Bessel function's pathway fractional integral operator. The following noteworthy special cases have been brought forward for consideration. The pathway transform of the generalized Bessel function has also been developed.
The use of fractional kinetic equations to describe the many phenomena regulated by anomalous rea... more The use of fractional kinetic equations to describe the many phenomena regulated by anomalous reactions in dynamical systems with chaotic motion is examined. Several authors have used a variety of methodologies to study a number of difficulties arising from the generalised Bessel's function. In this follow-up study, the results of Katugampola kinetic fractional equations containing the first kind of generalised Bessel's function will be investigated. The result is obtained using the τ Laplace transform technique. We may use the generality of this series to deduce solutions for a fractional kinetic equation employing a different sort of Bessel's series. A graphical representation of the behaviors of the obtained solutions is also supplied.
In this paper we have reviewed and presented the results of the fractional order differential fie... more In this paper we have reviewed and presented the results of the fractional order differential field equation for a Bianchi type-II (LRS) space-time with a perfect fluid assuming a variable cosmological constant Λ (adopted from R. K. Tiwari et. al.[13]). In order to substitute Einstein's field equations for a certain configuration with equivalent fractional field equations, we used the Last Step Modification (LSM) method. Further applied Riemann-Liouville fractional order derivative assuming lower terminal at 0 to obtain all physical properties of the developed model along with their graphical representation.
The aim of this paper is to obtain a solution of integral equation of the Saigo-Maeda operator wh... more The aim of this paper is to obtain a solution of integral equation of the Saigo-Maeda operator which contain Appell-hypergeometric function as a kernel. The integral equation and its solution gives new form of generalised fractional integral and generalised fractional derivative. Further various consequences also investigated.
Applications and Applied Mathematics: An International Journal (AAM), 2016
In this paper, we study the extended Mittag-Leffler function by using generalized beta function a... more In this paper, we study the extended Mittag-Leffler function by using generalized beta function and obtain various differential properties, integral representations. Further, we discuss Mellin transform of these functions in terms of generalized Wright hyper geometric function and evaluate Laplace transform, and Whittaker transform in terms of extended beta function. Finally, several interesting special cases of extended Mittag-Leffler functions have also be given.
This paper is devoted to the study of ψ-generalized Mittag-Leffler function associated with ψ-gen... more This paper is devoted to the study of ψ-generalized Mittag-Leffler function associated with ψ-generalized beta function. We also obtain integral representations and other useful properties of it for example, Mellin transforms, recurrence relations etc. Further we develop derivative formulas and some fractional differ-integral properties for this ψ-generalized Mittag-Leffler function. Other than this we also establish fractional integral operator containing ψ-generalized Mittag-Leffler function as its kernel and obtain some associated properties.Publisher's Versio
In this research work our aim is to determine some contiguous relations and some integral transfo... more In this research work our aim is to determine some contiguous relations and some integral transform of the k-generalised hypergeometric functions, by using the concept of “k-Gamma and k-Beta function”. “Obviously if k approaches 1”, then the contiguous function relations become Gauss contiguous relations
The focus of this research is to use a new extended beta function and develop the extensions of G... more The focus of this research is to use a new extended beta function and develop the extensions of Gauss hypergeometric functions and confluent hypergeometric function formulas that are presumed to be new. Four theorems have also been defined under the generalized fractional integral operators that provide an image formula for the extension of new Gauss hypergeometric functions and the extension of new confluent hypergeometric functions. Moreover, discussed are analogous statements in terms of the Weyl, Riemann–Liouville, Erdélyi–Kober, and Saigo fractional integral and derivative operator types. Here, we are also able to generate more image formulas by keeping some integral transforms on the obtained formulas.
In this paper, we study the extended Mittag -Leffler function by using generalized beta function ... more In this paper, we study the extended Mittag -Leffler function by using generalized beta function and obtain various differential properties, integral representations. Further, we discuss Mellin transform of these functions in terms of generalized Wright hyper geometric function and evaluate Laplace transform, and Whittaker transform in terms of extended beta function. Finally, several interesting special cases of extended Mittag -Leffler functions have also be given
The purpose of this research is to provide a systematic review of a new type of extended beta fun... more The purpose of this research is to provide a systematic review of a new type of extended beta function and hypergeometric function using a confluent hypergeometric function, as well as to examine various belongings and formulas of the new type of extended beta function, such as integral representations, derivative formulas, transformation formulas, and summation formulas. In addition, we also investigate extended Riemann–Liouville (R-L) fractional integral operator with associated properties. Furthermore, we develop new beta distribution and present graphically the relation between moment generating function and ℓ .
Abstract: In this paper we first establish the two new functions St(λ1,...,λ2, p, a, b1,...,bn) a... more Abstract: In this paper we first establish the two new functions St(λ1,...,λ2, p, a, b1,...,bn) and St(λ1,... ,λn, q, a, b1,... ,bn) using generalized Lauricella function [7] then we discuss the fractional integral and differential properties, integral representations and Laplace transform of these functions. Further we have mentioned the particular cases of our results which are new & interesting by themselves.
South East Asian J of Mathematics and Mathematical Sciences, Aug 29, 2023
The current study aims to describe the generalized Bessel function's pathway fractional integral ... more The current study aims to describe the generalized Bessel function's pathway fractional integral operator. The following noteworthy special cases have been brought forward for consideration. The pathway transform of the generalized Bessel function has also been developed.
The use of fractional kinetic equations to describe the many phenomena regulated by anomalous rea... more The use of fractional kinetic equations to describe the many phenomena regulated by anomalous reactions in dynamical systems with chaotic motion is examined. Several authors have used a variety of methodologies to study a number of difficulties arising from the generalised Bessel's function. In this follow-up study, the results of Katugampola kinetic fractional equations containing the first kind of generalised Bessel's function will be investigated. The result is obtained using the τ Laplace transform technique. We may use the generality of this series to deduce solutions for a fractional kinetic equation employing a different sort of Bessel's series. A graphical representation of the behaviors of the obtained solutions is also supplied.
In this paper we have reviewed and presented the results of the fractional order differential fie... more In this paper we have reviewed and presented the results of the fractional order differential field equation for a Bianchi type-II (LRS) space-time with a perfect fluid assuming a variable cosmological constant Λ (adopted from R. K. Tiwari et. al.[13]). In order to substitute Einstein's field equations for a certain configuration with equivalent fractional field equations, we used the Last Step Modification (LSM) method. Further applied Riemann-Liouville fractional order derivative assuming lower terminal at 0 to obtain all physical properties of the developed model along with their graphical representation.
The aim of this paper is to obtain a solution of integral equation of the Saigo-Maeda operator wh... more The aim of this paper is to obtain a solution of integral equation of the Saigo-Maeda operator which contain Appell-hypergeometric function as a kernel. The integral equation and its solution gives new form of generalised fractional integral and generalised fractional derivative. Further various consequences also investigated.
Applications and Applied Mathematics: An International Journal (AAM), 2016
In this paper, we study the extended Mittag-Leffler function by using generalized beta function a... more In this paper, we study the extended Mittag-Leffler function by using generalized beta function and obtain various differential properties, integral representations. Further, we discuss Mellin transform of these functions in terms of generalized Wright hyper geometric function and evaluate Laplace transform, and Whittaker transform in terms of extended beta function. Finally, several interesting special cases of extended Mittag-Leffler functions have also be given.
This paper is devoted to the study of ψ-generalized Mittag-Leffler function associated with ψ-gen... more This paper is devoted to the study of ψ-generalized Mittag-Leffler function associated with ψ-generalized beta function. We also obtain integral representations and other useful properties of it for example, Mellin transforms, recurrence relations etc. Further we develop derivative formulas and some fractional differ-integral properties for this ψ-generalized Mittag-Leffler function. Other than this we also establish fractional integral operator containing ψ-generalized Mittag-Leffler function as its kernel and obtain some associated properties.Publisher's Versio
In this research work our aim is to determine some contiguous relations and some integral transfo... more In this research work our aim is to determine some contiguous relations and some integral transform of the k-generalised hypergeometric functions, by using the concept of “k-Gamma and k-Beta function”. “Obviously if k approaches 1”, then the contiguous function relations become Gauss contiguous relations
The focus of this research is to use a new extended beta function and develop the extensions of G... more The focus of this research is to use a new extended beta function and develop the extensions of Gauss hypergeometric functions and confluent hypergeometric function formulas that are presumed to be new. Four theorems have also been defined under the generalized fractional integral operators that provide an image formula for the extension of new Gauss hypergeometric functions and the extension of new confluent hypergeometric functions. Moreover, discussed are analogous statements in terms of the Weyl, Riemann–Liouville, Erdélyi–Kober, and Saigo fractional integral and derivative operator types. Here, we are also able to generate more image formulas by keeping some integral transforms on the obtained formulas.
In this paper, we study the extended Mittag -Leffler function by using generalized beta function ... more In this paper, we study the extended Mittag -Leffler function by using generalized beta function and obtain various differential properties, integral representations. Further, we discuss Mellin transform of these functions in terms of generalized Wright hyper geometric function and evaluate Laplace transform, and Whittaker transform in terms of extended beta function. Finally, several interesting special cases of extended Mittag -Leffler functions have also be given
The purpose of this research is to provide a systematic review of a new type of extended beta fun... more The purpose of this research is to provide a systematic review of a new type of extended beta function and hypergeometric function using a confluent hypergeometric function, as well as to examine various belongings and formulas of the new type of extended beta function, such as integral representations, derivative formulas, transformation formulas, and summation formulas. In addition, we also investigate extended Riemann–Liouville (R-L) fractional integral operator with associated properties. Furthermore, we develop new beta distribution and present graphically the relation between moment generating function and ℓ .
Abstract: In this paper we first establish the two new functions St(λ1,...,λ2, p, a, b1,...,bn) a... more Abstract: In this paper we first establish the two new functions St(λ1,...,λ2, p, a, b1,...,bn) and St(λ1,... ,λn, q, a, b1,... ,bn) using generalized Lauricella function [7] then we discuss the fractional integral and differential properties, integral representations and Laplace transform of these functions. Further we have mentioned the particular cases of our results which are new & interesting by themselves.
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