Description:
Frontmatter -- Preface -- Contents -- 1 Fractional derivatives and numerical approximations -- 2 Difference methods for the time-fractional subdiffusion equations -- 3 Difference methods for the time-fractional wave equations -- 4 Difference methods for the space-fractional partial differential equations -- 5 Difference methods for the time-space-fractional differential equations -- 6 Difference methods for the time distributed-order subdiffusion equations -- A The Matlab code of sum-of-exponentials approximations for the kernel t−α in the Caputo fractional derivative -- Bibliography -- Index
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