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Fractional Calculus

  • Ricardo Almeida
  • Dina Tavares
  • Delfim F. M. TorresEmail author
Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

In this chapter, a brief introduction to the theory of fractional calculus is presented. We start with a historical perspective of the theory, with a strong connection with the development of classical calculus (Sect. 1.1). Then, in Sect. 1.2, we review some definitions and properties about a few special functions that will be needed. We end with a review on fractional integrals and fractional derivatives of noninteger order and with some formulas of integration by parts, involving fractional operators (Sect. 1.3).

Keywords

Variable-order Fractional Calculus Caputo Fractional Derivative Fractional Integral Odzijewicz Riemann Liouville 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Author(s), under exclusive license to Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Ricardo Almeida
    • 1
  • Dina Tavares
    • 2
  • Delfim F. M. Torres
    • 1
    Email author
  1. 1.Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.Polytechnic Institute of LeiriaLeiriaPortugal

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