Introduction to fractional integrability and differentiability

摘要

In this paper, we mainly consider fractional integral and derivatives including the Riemann-Liouville derivative, Caputo derivative, Gr¨unwald-Letnikov derivative, Marchaud derivative, Riesz derivative, local fractional derivative, Canavati derivative. Then we introduce their existence conditions. Important issues on these fractional integral and derivatives are also included.