Milos Ilic

Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions

In this paper, a time-space fractional diffusion equation in two dimensions (TSFDE-2D) with homogeneous Dirichlet boundary conditions is considered. The TSFDE-2D is obtained from the standard diffusion equation by replacing the first-order time derivative with the Caputo fractional derivative

Convective drying of a consolidated slab of wet porous material

_{t}D_{*}^{\gamma}

Convective drying of a consolidated slab of wet porous material including the sorption region

,

Drying of a wet porous material

\gamma\in(0,1)

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

, and the second-order space derivatives with the fractional Laplacian

Analytical and numerical solutions of a one-dimensional fractional-in-space diffusion equation in a composite medium

-(-\Delta)^{\alpha/2}

Krylov subspaces and the analytic grade

,

Modelling non-fickian behavior in the cell walls of wood using a fractional-in-space diffusion equation

\alpha\in(1,2]

A CONTINUUM MODEL OF DRYING PROCESSES INVOLVING A JUMP THROUGH HYSTERESIS

. Using the matrix transfer technique proposed by Ilic et al. [M. Ilic, F. Liu, I. Turner, and V. Anh, Fract. Calc. Appl. Anal., 9 (2006), pp. 333-349], the TSFDE-2D is transformed into a time fractional differential system as

Linear system solution by null‐space approximation and projection (SNAP)

_{t}D_{*}^{\gamma}\mathbf{u} = -K_\alpha\mathbf{A}^{\alpha/2}\mathbf{u}