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H.J. Haubold

  1. Computable solutions of fractional partial differential equations related to reaction-diffusion systems.

    Пнд, 10/03/2011 - 15:01 — SomNambul
    Authors: H.J. Haubold, A.M. Mathai, R.K. Saxena
    Subjects: Mathematical Physics
    Abstract

    The object of this paper is to present a computable solution of a fractional
    partial differential equation associated with a Riemann-Liouville derivative of
    fractional order as the time-derivative and Riesz-Feller fractional derivative
    as the space derivative. The method followed in deriving the solution is that
    of joint Laplace and Fourier transforms. The solution is derived in a closed
    and computable form in terms of the H-function. It provides an elegant
    extension of the results given earlier by Debnath, Chen et al., Haubold et al.,
    Mainardi et al., Saxena et al., and Pagnini et al.

  2. Solutions of the Fractional Reaction Equation and the Fractional Diffusion Equation.

    Чт, 01/14/2010 - 16:01 — SomNambul
    Authors: H.J. Haubold, A.M. Mathai, R.K. Saxena
    Subjects: Mathematical Physics
    Abstract

    In view of the role of reaction equations in physical problems, the authors
    derive the explicit solution of a fractional reaction equation of general
    character, that unifies and extends earlier results. Further, an alternative
    shorter method based on a result developed by the authors is given to derive
    the solution of a fractional diffusion equation. Fox functions and
    Mittag-Leffler functions are used for closed-form representations of the
    solutions of the respective differential equations.

  3. Extended Reaction Rate Integral as Solutions of Some General Differential Equations.

    Чт, 01/14/2010 - 16:01 — SomNambul
    Authors: H.J. Haubold, D.P. Joseph
    Subjects: Mathematical Physics
    Abstract

    Here an extended form of the reaction rate probability integral, in the case
    of nonresonant thermonuclear reactions with the depleted tail and the right
    tail cut off, is considered. The reaction rate integral then can be looked upon
    as the inverse of the convolution of the Mellin transforms of Tsallis type
    statistics of nonextensive statistical mechanics and stretched exponential as
    well as that of superstatistics and stretched exponentials. The differential
    equations satisfied by the extended probability integrals are derived.

  4. An Alternative Method for Solving a Certain Class of Fractional Kinetic Equations.

    Чт, 01/14/2010 - 16:01 — SomNambul
    Authors: H.J. Haubold, A.M. Mathai, R.K. Saxena
    Subjects: Mathematical Physics
    Abstract

    An alternative method for solving the fractional kinetic equations solved
    earlier by Haubold and Mathai (2000) and Saxena et al. (2002, 2004a, 2004b) is
    recently given by Saxena and Kalla (2007). This method can also be applied in
    solving more general fractional kinetic equations than the ones solved by the
    aforesaid authors.

  5. Mittag-Leffler Functions and Their Applications.

    Ср, 09/02/2009 - 12:02 — SomNambul
    Authors: H.J. Haubold, A.M. Mathai, R.K. Saxena
    Subjects: Classical Analysis and ODEs
    Abstract

    Motivated essentially by the success of the applications of the
    Mittag-Leffler functions in many areas of science and engineering, the authors
    present in a unified manner, a detailed account or rather a brief survey of the
    Mittag- Leffler function, generalized Mittag-Leffler functions, Mittag-Leffler
    type functions, and their interesting and useful properties. Applications of
    Mittag-Leffler functions in certain areas of physical and applied sciences are
    also demonstrated.

  6. Mittag-Leffler Functions and Their Applications.

    Ср, 09/02/2009 - 12:02 — SomNambul
    Authors: H.J. Haubold, A.M. Mathai, R.K. Saxena
    Subjects: Classical Analysis and ODEs
    Abstract

    Motivated essentially by the success of the applications of the
    Mittag-Leffler functions in many areas of science and engineering, the authors
    present in a unified manner, a detailed account or rather a brief survey of the
    Mittag- Leffler function, generalized Mittag-Leffler functions, Mittag-Leffler
    type functions, and their interesting and useful properties. Applications of
    Mittag-Leffler functions in certain areas of physical and applied sciences are
    also demonstrated.

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