Application of Fractional Derivative Operators to Anomalous Diffusion and Propagation Problems

Details Application of Fractional Derivative Operators to Anomalous Diffusion and Propagation Problems Application of Fractional Derivative Operators to Anomalous Diffusion and Propagation Problems

2007-01-28

arxiv.org/abs/math-ph/0701068v2

Physics

Mathematical Physics

11 pages, 4 figure This research is supported by KBN grant 2PO3B-126- 24

Scientific paper

We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations account for typical "anomalous" features which are observed in many systems, e.g. in the case of dispersive transport in amorphous semiconductors, liquid crystals, polymers, proteins and biosystems. In contrast to Gaussian diffusion, fractional diffusion is related to LEVY STABLE NON-GAUSSIAN PROCESSES. The typical features of the processes are heavy tails of probability density distributions. Conservation laws in relation to fractional operators are discussed. The next objective of this paper is an application of main rules of fractional calculus, fractional Laplacians, factorization of the Helmholtz equation to obtain four pairs of fractional eigenfunctions allowing to construct a solution to the well known half-plane diffraction problems. Factorizing the Leontovich-Fock equation, (parabolic wave equation-PWE), we determine semi-differential fractional solutions, which allow us to find paraxial solutions for given beam boundary conditions.

Affiliated with

Also associated with

No associations

Rating

Application of Fractional Derivative Operators to Anomalous Diffusion and Propagation Problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Application of Fractional Derivative Operators to Anomalous Diffusion and Propagation Problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Application of Fractional Derivative Operators to Anomalous Diffusion and Propagation Problems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-197255