The fractional kinetic equation and thermonuclear functions

By Hans J. Haubold, Arak M. Mathai. 2000

187 citations recorded by the source corpus.

The paper discusses the solution of a simple kinetic equation of thetype used for the computation of the change of the chemical compositionin stars like the Sun. Starting from the standard form of the kineticequation it is generalized to a fractional kinetic equation and itssolutions in terms of H-functions are obtained. The role of thermonuclearfunctions, which are also represented in terms of G- and H-functions,in such a fractional kinetic equation is emphasized. Results containedin this paper are related to recent investigations of possibleastrophysical solutions of the solar neutrino problem.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2c58eaa1ba812e19d90637018e3ce8a2a73e73f1

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Citations in the corpus

Fractional Calculus involving (p, q)-Mathieu Type Series (2020, methodology): “If we remove the index i and integrate the standard kinetic equation (4.2), we have N(t)−N0 =−c0D−1t N(t) (4.3) where 0D−1t is the special case of the Riemann-Liouville integral operator 0D −ν t defined as 0D−νt f (t) = 1 Γ(ν) ˆ t 0 (t− s)ν−1 f (s)ds, (t > 0,R(ν)> 0) (4.4) The fractional generalizat”
Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy (2006, background): “Now, consider an equation parallel to equation (17) in Mathai, Saxena, and Haubold (2005), namely, for γ > 0 , c > 0 , ν > 0 , µ > 0.”
On fractional kinetic equations (2002, methodology): “By dropping the index i in (10), the solution of its generalized form N(t)−N0 = −c ν 0D −ν t N(t), (11) is obtained (Haubold and Mathai, 2000) as N(t) = N0 ∞ ∑ k=0 (−1)k(ct)νk Γ(νk + 1) , (12) By virtue of (2) we can rewrite (12) in terms of the Mittag-Leffler function in a compact form as N(t) =…”
Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments (2020, background): “This may be formally represented by the following equation (see [26]):”
On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind (2015, background): “Haubold and Mathai [13] have established a functional differential equation between rate of change of reaction, the destruction rate, and the production rate as follows:”