Unified Fractional Kinetic Equation and a Fractional Diffusion Equation

Abstract

In earlier papers Saxena et al. (2002, 2003) derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which extended the work of Haubold and Mathai (2000). The object of the present paper is to investigate the solution of a unified form of fractional kinetic equation in which the free term contains any integrable function f(t), which provides the unification and extension of the results given earlier recently by Saxena et al. (2002, 2003). The solution has been developed in terms of the Wright function in a closed form by the method of Laplace transform. Further we derive a closed-form solution of a fractional diffusion equation. The asymptotic expansion of the derived solution with respect to the space variable is also discussed. The results obtained are in a form suitable for numerical computation.

13 pages, LaTeX

References in corpus (1)

• On Fractional Kinetic Equations

Cited by in corpus (17)

• Fractional reaction-diffusion equations
• On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics
• Solution of generalized fractional reaction-diffusion equations
• Comb model with slow and ultraslow diffusion
• Reaction-diffusion systems and nonlinear waves
• Models for characterizing the transition among anomalous diffusions with different diffusion exponents
• Fractional Non-Linear, Linear and Sublinear Death Processes
• Generalized Mittag-Leffler functions in the theory of finite-size scaling for systems with strong anisotropy and/or long-range interaction
• Analysis of Solar Neutrino Data from SuperKamiokande I and II: Back to the Solar Neutrino Problem
• Solutions of certain fractional kinetic equations and a fractional diffusion equation
• Space-time fractional reaction-diffusion equations associated with a generalized Riemann-Liouville fractional derivative
• Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling
• Generalized distributed order diffusion equations with composite time fractional derivative
• Fractional diffusion equations interpolate between damping and waves
• Solutions of the Fractional Reaction Equation and the Fractional Diffusion Equation
• Emergent time crystal from a fractional Langevin equation with white and colored noise
• An Alternative Method for Solving a Certain Class of Fractional Kinetic Equations