Eur. Phys. J. Special Topics 193, 5-26 (2011)
https://doi.org/10.1140/epjst/e2011-01378-2

Review

Introduction to fractional integrability and differentiability

Department of Mathematics, Shanghai University, Shanghai 200444, China

^a e-mail: lcp@shu.edu.cn
^b e-mail: zgzhao999@yahoo.com.cn

Received: 1 December 2010
Revised: 27 January 2011
Published online: 4 April 2011

Abstract

In this paper, we mainly consider fractional integral and derivatives including the Riemann-Liouville derivative, Caputo derivative, Grünwald-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.