Fractional Calculus

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


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).


Variable-order Fractional Calculus Caputo Fractional Derivative Fractional Integral Odzijewicz Riemann Liouville 
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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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