Rahul Goyal
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Rahul Goyal has a total of 10 co-authors. Here are the top co-authors by number of shared publications:
- Praveen Agarwal
Department of Mathematics, Anand International College of Engineering, Jaipur, India
7 shared publications - Shilpi Jain
Department of Mathematics, Poornima College of Engineering, Jaipur, India
5 shared publications - Clemente Cesarano
Section of Mathematics, International Telematic University Uninettuno, Roma, Italy
3 shared publications - Shaher Momani
Nonlinear Dynamics Research Center (NDRC) Ajman University Ajman UAE
2 shared publications - Alexandra Parmentier
INAF, Istituto di Astrofisica e Planetologia Spaziali, Rome, Italy
1 shared publication - Antonella Lupica
Department of Economics, Engineering, Society and Business Organization (DEIm), University of Tuscia, Largo dell’Università, 01100 Viterbo, Italy
1 shared publication
Latest Publications
- 1 June 2023
- Published by Pleiades Publishing Ltd in Lobachevskii Journal of Mathematics
- Vol. 44 (6) , 2269-2278
On a New Class of Hypergeometric Function
The major objective of this article is to establish a new function called \({}_{p}G_{q}^{\eta,\zeta,m,\xi}(z)\) which is generalization of the generalized hypergeometric function and Mittag-Leffler function and obtain its properties particular differential property, integral representation, derivative formula and some integral transform, Euler transform, Laplace transform, Whittaker transform. We also derived the relations that exist between \({}_{p}G_{q}^{\eta,\zeta,m,\xi}(z)\) function with well known special functions. This article also deals with some fractional integral properties of the \({}_{p}G_{q}^{\eta,\zeta,m,\xi}(z)\) function using the Riemann–Liouville fractional integrals and derivatives operators.- 1 June 2023
- Published by Pleiades Publishing Ltd in Lobachevskii Journal of Mathematics
- Vol. 44 (6) , 2269-2278
On a New Class of Hypergeometric Function
The major objective of this article is to establish a new function called \({}_{p}G_{q}^{\eta,\zeta,m,\xi}(z)\) which is generalization of the generalized hypergeometric function and Mittag-Leffler function and obtain its properties particular differential property, integral representation, derivative formula and some integral transform, Euler transform, Laplace transform, Whittaker transform. We also derived the relations that exist between \({}_{p}G_{q}^{\eta,\zeta,m,\xi}(z)\) function with well known special functions. This article also deals with some fractional integral properties of the \({}_{p}G_{q}^{\eta,\zeta,m,\xi}(z)\) function using the Riemann–Liouville fractional integrals and derivatives operators.- Open Access
- 23 January 2023
- Published by AccScience Publishing in An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
- Vol. 13 (1) , 1-9
Certain saigo type fractional integral inequalities and their q-analogues
The main purpose of the present article is to introduce certain new Saigo fractional integral inequalities and their q-extensions. We also studied some special cases of these inequalities involving Riemann-Liouville and Erdelyi-Kober fractional integral operators.
- 23 January 2023
- Published by AccScience Publishing in An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
- Vol. 13 (1) , 1-9
Open AccessCertain saigo type fractional integral inequalities and their q-analogues
The main purpose of the present article is to introduce certain new Saigo fractional integral inequalities and their q-extensions. We also studied some special cases of these inequalities involving Riemann-Liouville and Erdelyi-Kober fractional integral operators.
- Open Access
- 11 March 2022
- Published by MDPI AG in Mathematics
- Vol. 10 (6) , 892
Extended Beta and Gamma Matrix Functions via 2-Parameter Mittag-Leffler Matrix Function
The main aim of this article is to study an extension of the Beta and Gamma matrix functions by using a two-parameter Mittag-Leffler matrix function. In particular, we investigate certain properties of these extended matrix functions such as symmetric relation, integral representations, summation relations, generating relation and functional relation.
- 11 March 2022
- Published by MDPI AG in Mathematics
- Vol. 10 (6) , 892
Open AccessExtended Beta and Gamma Matrix Functions via 2-Parameter Mittag-Leffler Matrix Function
The main aim of this article is to study an extension of the Beta and Gamma matrix functions by using a two-parameter Mittag-Leffler matrix function. In particular, we investigate certain properties of these extended matrix functions such as symmetric relation, integral representations, summation relations, generating relation and functional relation.
- Open Access
An Extension of Caputo Fractional Derivative Operator by Use of Wiman’s Function
The main aim of this work is to study an extension of the Caputo fractional derivative operator by use of the two-parameter Mittag–Leffler function given by Wiman. We have studied some generating relations, Mellin transforms and other relationships with extended hypergeometric functions in order to derive this extended operator. Due to symmetry in the family of special functions, it is easy to study their various properties with the extended fractional derivative operators.
Open AccessAn Extension of Caputo Fractional Derivative Operator by Use of Wiman’s Function
The main aim of this work is to study an extension of the Caputo fractional derivative operator by use of the two-parameter Mittag–Leffler function given by Wiman. We have studied some generating relations, Mellin transforms and other relationships with extended hypergeometric functions in order to derive this extended operator. Due to symmetry in the family of special functions, it is easy to study their various properties with the extended fractional derivative operators.
- Open Access
- 18 November 2021
- Published by MDPI AG in Mathematics
- Vol. 9 (22) , 2944
Some Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function
The main aim of this research paper is to introduce a new extension of the Gauss hypergeometric function and confluent hypergeometric function by using an extended beta function. Some functional relations, summation relations, integral representations, linear transformation formulas, and derivative formulas for these extended functions are derived. We also introduce the logarithmic convexity and some important inequalities for extended beta function.
- 18 November 2021
- Published by MDPI AG in Mathematics
- Vol. 9 (22) , 2944
Open AccessSome Results of Extended Beta Function and Hypergeometric Functions by Using Wiman’s Function
The main aim of this research paper is to introduce a new extension of the Gauss hypergeometric function and confluent hypergeometric function by using an extended beta function. Some functional relations, summation relations, integral representations, linear transformation formulas, and derivative formulas for these extended functions are derived. We also introduce the logarithmic convexity and some important inequalities for extended beta function.
- Open Access
- 25 October 2021
- Published by MDPI AG in Mathematics
- Vol. 9 (21) , 2702
Some Inequalities of Extended Hypergeometric Functions
Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent hypergeometric function, respectively, by virtue of Hölder integral inequality and Chebyshev’s integral inequality. We also studied the monotonicity, log-concavity, and log-convexity of extended hypergeometric functions, which are derived by using the inequalities on an extended beta function.
- 25 October 2021
- Published by MDPI AG in Mathematics
- Vol. 9 (21) , 2702
Open AccessSome Inequalities of Extended Hypergeometric Functions
Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent hypergeometric function, respectively, by virtue of Hölder integral inequality and Chebyshev’s integral inequality. We also studied the monotonicity, log-concavity, and log-convexity of extended hypergeometric functions, which are derived by using the inequalities on an extended beta function.
- Open Access
An Extension of Beta Function by Using Wiman’s Function
The main purpose of this paper is to study extension of the extended beta function by Shadab et al. by using 2-parameter Mittag-Leffler function given by Wiman. In particular, we study some functional relations, integral representation, Mellin transform and derivative formulas for this extended beta function.
Open AccessAn Extension of Beta Function by Using Wiman’s Function
The main purpose of this paper is to study extension of the extended beta function by Shadab et al. by using 2-parameter Mittag-Leffler function given by Wiman. In particular, we study some functional relations, integral representation, Mellin transform and derivative formulas for this extended beta function.