Numerical methods for fractional differential equations - Li, Xuhao (2018)
Fractional differential equations have received much attention in recent decades likely due to its powerful ability in modeling `memory' processes, which are mostly observed in real world. Fractional models have been widely investigated and applied in many fields such as physics, biochemistry, electrical engineering, continuum and statistical mechanics. It is shown by many researchers that fractional derivatives can provide more accurate models than integer order derivatives do. However, for most models involving fractional operators, it is very challenging if not impossible to get analytical solutions. This motivates us to propose numerical techniques, especially those that can obtain numerical approximations both efficiently and effectively.