Hans J. Haubold

Further solutions of fractional reaction-diffusion equations in terms of the H-function

This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the Laplace and Fourier transforms in closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by many authors, notably by Mainardi et al. (2001, 2005) for the fundamental solution of the space-time fractional diffusion equation, and Saxena et al. (2006a, b) for fractional reaction- diffusion equations. The advantage of using Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation containing this derivative includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of neutral fractional diffusion, space-fractional diffusion, and time-fractional diffusion. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-functions in compact form.

Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

Geometric generalized Mittag-Leffler distributions having the Laplace transform \(\frac{1} {1+\beta \log (1+{t}^{\alpha })},0 0\) is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (Astrophysics and Space Science 273 53–63, 2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al. (2002; Astrophysics and Space Science 209 299–310 2004a; Physica A 344 657–664 2004b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.

Kunitomo Sakurai, Solar Neutrino Problems â How they were Solved

Hans J. Haubold1,2* and Arak M. Mathai1,3 1Centre for Mathematical and Statistical Sciences, Peechi Campus, KFRI, Peechi-680653, Kerala, India 2Office for Outer Space Affairs, United Nations, P.O. Box 500, Vienna International Center, A-1400 Vienna, Austria 3Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, Canada *Corresponding author: Hans J. Haubold, Office for Outer Space Affairs, United Nations, P.O. Box 500, Vienna International Center, A-1400 Vienna, Austria, Tel: +43-1-260 60 4950; E-mail: hans.haubold@gmail.com

DIVISION XII / COMMISSION 46 / PROGRAM GROUP COLLABORATIVE PROGRAMMES

2.1. Sinaia, Romania, 4–16 June 2007. Solar-Terrestrial Interactions (STIINTE) This Workshop, organized by Joachim Vogt and Octav Marghitu, was dedicated to the analysis of data from multi-satellite space missions such as Cluster. It was attended by 24 very motivated PhD students and post-docs coming from Central and Eastern Europe: Romania, Hungary, Bulgaria, Czech Republic, Poland, Ukraine, Russia, Armenia, and Georgia. The scientific programme focused on various aspects of multi-satellite missions, ranging from data analysis and instrument design to kinetic modeling, the analysis of boundaries, and the analysis of auroral processes. After a first and already quite intensive week, the work culminated in the preparation of scientific projects by five teams. Each team had to address a specific problem in magnetospheric physics, leading to very intensive team-work and providing an excellent opportunity for the students to interact, put together their competences and apply what had been learned. On the last day of the school, each team defended its project to a panel of senior scientists who were participating at the simultaneous Solar Terrestrial Interactions from Microscales to Global Models (STIMM-2) meeting. The Workshop took place in the framework of the Plan for European Cooperating State (PECS) agreement between Romania and ESA, which is designed to prepare for full Romanian membership of ESA.