Reaction?Diffusion Problems in the Physics of Hot Plasmas

2006

Abstract. In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen, Metzler, and Fogedby (1999) for anomalous diffusion and del-Castillo-Negrete, Carreras, and Lynch (2003)

Section: Discussionmentioning

confidence: 99%

“…Reaction-diffusion models have found numerous applications in pattern formation in biology, chemistry, and physics, see Murray (2003), Kuramoto (2003), Wilhelmsson and Lazzaro (2001), and Hundsdorfer and Verwer (2003). These systems indicate that diffusion can produce spontaneous formation of spatio-temporal patterns.…”

Section: Introductionmentioning

confidence: 99%

Fractional Reaction-Diffusion Equations

2006

“…and physics, see Wilhelmsson and Lazzaro (2001) and Frank (2005). These systems indicate that diffusion can produce the spontaneous formation of spatio-temporal patterns.…”

Section: Introductionmentioning

confidence: 99%

Solution of Generalized Fractional Reaction-Diffusion Equations

2006

“…Linear and nonlinear reaction, diffusion, and reaction-diffusion equations, respectively, are used to model spatio-temporal processes in physical systems, for example astrophysical fusion plasmas (Wilhelmsson and Lazzaro, 2001;Kulsrud, 2005) . Such equations give rise to dissipative structures and self-organization phenomena (Nicolis and Prigogine, 1977;Haken 2004).…”

Section: Discussionmentioning

confidence: 99%

A Certain Class of Laplace Transforms with Applications to Reaction and Reaction-Diffusion Equations

2006

Abstract. A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables and the concept of Laplacianness in statistics, α-Laplace and Mittag-Leffler stochastic processes, the concepts of infinite divisibility and geometric infinite divisibility problems in probability theory and certain fractional integrals and fractional derivatives. A number of applications are pointed out with special reference to solutions of fractional reaction and reaction-diffusion equations and their generalizations.