Solution of Generalized Fractional Reaction-Diffusion Equations

Abstract

Abstract. This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.

Analysis of Solar Neutrino Data from Super-Kamiokande I and II

“…The probability density function for the above Super-Kamiokande data is non-Gaussian and exhibits stretched power-law tails, as can be shown by further exploring Equations (6), (9) and (12). In order to model these analytic findings, a transport model for the pdf, based on fractional diffusion, which includes both non-local and non-Gaussian features, was proposed [26].…”

“…Both the translation of the standard reaction Equation (7) to a fractional reaction Equation (8) and the probabilistic interpretation of such equations lead to deviations from the exponential behavior to the power law behavior expressed in terms of Mittag-Leffler functions (9) or, as can be shown for Equation (12), to power law behavior in terms of H-functions [26]. H-functions are representable in terms of Mellin-Barnes integrals of the product of gamma functions and are therefore suited to represent statistics of products and quotients of independent random variables, thus providing a very useful tool in presenting a new perspective on the statistics of random variables [42].…”

“…This paper summarizes briefly a research programme, comprised of five elements: (i) standard deviation analysis and diffusion entropy analysis of solar neutrino data [1,2]; (ii) Mathai's entropic pathway model [3,4]; (iii) fractional reaction and extended thermonuclear functions [5,6]; (iv) fractional reaction and diffusion [7,8]; and (v) fractional reaction-diffusion [9][10][11][12]. Boltzmann translated Clausius' second law of thermodynamics "The entropy of the Universe tends to a maximum" into a crucial quantity that links equilibrium and non-equilibrium (time dependent) properties of physical systems and related entropy to probability, S = k log W, which, later, Einstein called Boltzmann's principle [13].…”

Solutions of Generalized Fractional Kinetic Equations via Sumudu Transforms Involving Bessel-Struve Kernel Function

“…The details about fractional kinetic equations and solutions, one can refer to [11,[17][18][19][20][21][22][23][24][25]30] 3. Solution of generalized fractional Kinetic equations involving (1.…”

Analytical predictions of non-Gaussian distribution parameters for stellar plasmas

“…In particular, there has been a great effort in this field to construct a statistical mechanics capable of describing systems affected by nonlocal and memory effects. Relevance of these problems in astrophysics and space science has been widely discussed in many papers by Saxena et al (2004Saxena et al ( , 2006) (see also Mathai and Haubold 2007;Haubold and Kumar 2007 for comments on applications of q-Gaussians in the above field).…”