Analytical solutions for anomalous transport of volatile pollutants in nonaqueous-phase liquid contaminated soil

Abstract

In this paper, we study a fractal model for the transport of a volatile component from a nonaqueous-phase liquids (NAPL) trapped in homogeneous soil. By introducing a kind of new integral transform in fractal space, analytical solutions of fractal model are given. Numerical results are presented graphically for various values of fractal dimension.

A Petrov-Galerkin Finite Element Method for Solving the Time-fractional Diffusion Equation with Interface

“…Fractional differential equations are generalized differential operations from integer orders to fractional derivative operations. The problem of fractional calculus has wide applications in fractal theory, signal processing, system control, quantum mechanics, environmental science, and finance (Jiang and Qi, 2010;Mainardi, 1996). The time-fractional differential equation is obtained by replacing the integer order in the classical model to fractional derivative, the fractional derivative at a certain time depends on all the values of the function before this time point, so the fractional partial differential equation is applicable for problems with memory process, genetic property and heterogeneous material (Rossikhin and Shitikova, 1997;Ichise et al, 1971).…”