Topic
Fox H-function
About: Fox H-function is a research topic. Over the lifetime, 39 publications have been published within this topic receiving 660 citations.
Papers
TL;DR: In this paper, a comparative study of modern differentiations based on singular versus non-singular and local versus nonlocal kernels have been analyzed for the free convection flow of Walter's-B liquid.
Abstract: In this research, a comparative study of modern differentiations based on singular versus non-singular and local versus non-local kernels have been analyzed for Walter’s-B liquid. In order to expose the efficiency of the two types of modern differentiations namely Caputo-Fabrizio and Atangana-Baleanu fractional differentiations, the partial differential equations governing Walter’s-B liquid are modeled through modern differentiations to study the free convection flow of Walter’s-B liquid. The critical focus is set on the combined heat and mass transfer. The fractional governing equations are solved by invoking the Laplace transform and general solutions are investigated for velocity, temperature and concentration analytically. The analytic solutions are transferred in terms of the Fox- H function for eliminating the gamma functions among the expressions of velocity, temperature and concentration. This comparative analysis indicates that the analytic results obtained via the Caputo-Fabrizio fractional differentiation have reciprocal trends in comparison with the Atangana-Baleanu fractional differentiation. Finally, graphical observations are also depicted for the check of influences of different pertinent parameters on the motion of Walter’s-B liquid.
93 citations
TL;DR: In this paper, an extension of the generalized inverse Gaussian density function is proposed, and several classical functions including, Abramowitz's functions, Dowson's integral function, Goodwin and Stalon's function, and astrophysical thermonuclear functions are proved to be special cases of these extensions.
75 citations
TL;DR: In this article, a Mittag-Leffler-type function of two variables E1 (x, y) and a generalization of Mittag Leffler type function of one variable as limiting case of E1 was studied.
Abstract: In this paper, we introduce and study a Mittag-Leffler-type function of two variables E1 (x, y) and a generalization of Mittag-Leffler-type function of one variable as limiting case of E1 (x, y), which includes several Mittag-Leffler-type functions of one variable as its special cases. Here, we first obtain the domain of convergence of E1 (x, y), considering all possible cases. Next, we give two differential equations for E1 (x, y) and one differential equation for for some particular values of the parameters. We further obtain two integral representations and Mellin–Barnes contour integral representation of E1 (x, y). We also obtain the Laplace transform of one and two dimensions of E1 (x, y) and its fractional integral and derivative. Next, we define an integral operator with E1 (x, y) as a kernel and show that it is bounded on the Lebesgue measurable space L(a, b). Finally, we introduce one more Mittag-Leffler-type function of two variables.
60 citations
TL;DR: In this paper, the authors derived simplified expressions for the luminosity density, cumulative luminosity and gravitational potential in terms of the Meijer G function for all rational values of the Sersic index, and investigated their asymptotic behaviour at small and large radii.
Abstract: The Sersic model has become the standard for parametrizing the surface brightness distribution of early-type galaxies and bulges of spiral galaxies. A major problem is that the deprojection of the Sersic surface brightness profile to a luminosity density cannot be executed analytically for general values of the Sersic index. We use Mellin integral transforms to derive an analytical expressions for the luminosity density in terms of the Fox H function for all values of the Sersic index. We derive simplified expressions for the luminosity density, cumulative luminosity, and gravitational potential in terms of the Meijer G function for all rational values of the Sersic index, and we investigate their asymptotic behaviour at small and large radii. As implementations of the Meijer G function are currently available both in symbolic computer algebra packages and as high-performance computing code, our results open up the possibility to calculate the density of the Sersic models to arbitrary precision.
56 citations
TL;DR: In this paper, the authors derived simplified expressions for the luminosity density, cumulative luminosity and gravitational potential in terms of the Meijer G function for all rational values of the Sersic index and investigated their asymptotic behaviour at small and large radii.
Abstract: The Sersic model has become the standard to parametrize the surface brightness distribution of early-type galaxies and bulges of spiral galaxies. A major problem is that the deprojection of the Sersic surface brightness profile to a luminosity density cannot be executed analytically for general values of the Sersic index. Mazure & Capelato (2002) used the Mathematica computer package to derive an expression of the Sersic luminosity density in terms of the Meijer G function for integer values of the Sersic index. We generalize this work using analytical means and use Mellin integral transforms to derive an exact, analytical expression for the luminosity density in terms of the Fox H function for all values of the Sersic index. We derive simplified expressions for the luminosity density, cumulative luminosity and gravitational potential in terms of the Meijer G function for all rational values of the Sersic index and we investigate their asymptotic behaviour at small and large radii. As implementations of the Meijer G function are nowadays available both in symbolic computer algebra packages and as high-performance computing code, our results open up the possibility to calculate the density of the Sersic models to arbitrary precision.
41 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 4 |
| 2019 | 5 |
| 2018 | 3 |
| 2017 | 1 |
| 2016 | 2 |