Guang-hua Gao & Zhi-Zhong Sun 
Fractional Differential Equations [PDF ebook] 
Finite Difference Methods

Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others. Approximation methods for fractional derivatives are developed and approximate accuracies are analyzed in detail.