Eur. Phys. J. Special Topics 222, 1827-1846 (2013)
https://doi.org/10.1140/epjst/e2013-01967-y

Review

Fractional calculus: A survey of useful formulas

¹ IDMEC / LAETA, Instituto Superior Técnico, Universidade de Lisboa, Portugal
² University of La Laguna, Departamento de Análisis Matemático, Tenerife, Spain
³ University of La Laguna, Departamento de Matemática Fundamental, Tenerife, Spain
⁴ Institute of Engineering of Polytechnic of Porto, Dept. of Electrical Engineering, Porto, Portugal
⁵ Çankaya University, Department of Mathematics and Computer Sciences, Balgat 06530, Ankara, Turkey
⁶ Institute of Space Sciences, Magurele-Bucharest, Romania
⁷ King Abdulaziz University, Department of Mathematics, Jeddah, Saudi Arabia

^a e-mail: duarte.valerio@ist.utl.pt
^b e-mail: jtrujill@ullmat.es
^c e-mail: mrivero@ull.es
^d e-mail: jtm@isep.ipp.pt
^e e-mail: dumitru.baleanu@gmail.com

Received: 3 June 2013
Revised: 6 August 2013
Published online: 7 October 2013

Abstract

This paper presents a survey of useful, established formulas in Fractional Calculus, systematically collected for reference purposes.