Concept of Fractional Divergence and Fractional Curl

Abstract

Fractional kinetic equations of the diffusion are useful approach for the description of transport dynamics in complex systems, which are governed by anomalous diffusion and non-exponential relaxation patterns. The anomalous diffusion can be modeled by fractional differential equation in time as well as space. For the spatial part use of fractional divergence modifies the anomalous diffusion expression, in the modified Fick’s law. Application of this fractional divergence is bought out in Nuclear reactor neutron flux definition. When anomalous diffusion is observed in time scale, the modification suggests use of Fractional kinetic equations. The evolution of Fractional Difference Equation, with reference to Fractional Brownian motion and the anomalous diffusion is also discussed in this chapter. Fractional curl operators will play perhaps role in electromagnetic theory and Maxwell equations. Here example in Electromagnetic is taken to have a feel how the fractional curl operator can map E and H fields in between the dual solutions of Maxwell equation.