Numerical methods for the solution of partial differential equations of fractional order
Journal of Computational Physics
Numerical solution of the space fractional Fokker-Planck equation
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
Finite difference approximations for fractional advection-dispersion flow equations
Journal of Computational and Applied Mathematics
Signal Processing - Fractional calculus applications in signals and systems
A second-order accurate numerical method for the two-dimensional fractional diffusion equation
Journal of Computational Physics
Journal of Computational Physics
Numerical solutions for fractional reaction-diffusion equations
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Matrix approach to discrete fractional calculus II: Partial fractional differential equations
Journal of Computational Physics
Hi-index | 0.02 |
Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain. We examine the case when a left-handed or a right-handed fractional spatial derivative may be present in the partial differential equation. Stability, consistency, and (therefore) convergence of the methods are discussed. The stability (and convergence) results in the fractional PDE unify the corresponding results for the classical parabolic and hyperbolic cases into a single condition. A numerical example using a finite difference method for a two-sided fractional PDE is also presented and compared with the exact analytical solution.