BACKGROUND Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. RESULTS The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carri...

Gas reservoirs with low permeability (k<0.1 mD) are among the unconventional reservoirs and are commonly termed as "Tight Gas Reservoirs". In conventional gas reservoirs that have high permeability, the flow of gas is basically controlled by the reservoir permeability and it is calculated using the Darcy equation. In these reservoirs, gas flow due to gas diffusion is ignored compared to Dar...

in this article, an analytical approximate solution of nonlinear fractional convection-diffusion with modifiedriemann-liouville derivative was obtained with the help of fractional variational iteration method (fvim). a newapplication of fractional variational iteration method (fvim) was extended to derive analytical solutions in theform of a series for this equation. it is indicated that the so...

in this paper, a modeling tool for risk assessment analysis of the movement of hydrocarbon contaminants in the vadose zone and mass flux of contamination release into the groundwater table was developed. also, advection-diffusion-reaction equations in combination with a three-phase equilibrium state between trapped air, soil humidity, and solid particles of unsaturated soil matrix were numerica...

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform m...