Many models are formulated in terms of fractional derivatives, such as in viscoelasticity, electrochemistry, electrode-electrolyte polarization, signal processing, diffusion processes, control processing, etc.
Differential equations with fractional derivative provided a natural framework for the discussion of various kinds of real problems modeled by the aid of fractional derivative, such as viscoelastic system, signal processing, diffusion processes, control processing, fractional stochastic system, allometry in biology and ecology (see [1, 4 7] and the references therein).
In image processing, the anisotropic diffusion process is equivalent to minimizing the following energy variational: E ( u ) = ∫ Ω [ β ( u - f ) 2 + t r ( ψ ( ∇ u ⋅ ∇ u T ) ) ] d x d y (1).
Next we will consider systems with signal transmission through external media, including diffusion processes, complex multicellular information processing and pattern formation.
However, recent years have been characterized by fast growing applications of fractional calculus to various scientific and engineering fields pertaining to anomalous diffusion, signal processing and control, constitutive modelling in viscoelasticity, image processing, fluid mechanics and findings on soft matter behavior, to mention a few.
These include diffusion during processing or in operation, the use of interface engineering to adjust band offsets, and the issues of crystallinity and of stoichiometry.
Mathematical methods for diffusion MRI processing.
After initial diffusion data processing, probabilistic tractography connectivity maps were systematically generated for 148 different anatomic regions in each hemisphere of the mouse brain (296 total).
Finally, the integration of nitride technology in devices may require lower growth temperature to avoid the potentially detrimental diffusion of species during processing.
