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Fractional Calculus

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The Variable-Order Fractional Calculus of Variations

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((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).

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Authors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Ricardo Almeida & Delfim F. M. Torres

  2. Polytechnic Institute of Leiria, Leiria, Portugal

    Dina Tavares

Authors
  1. Ricardo Almeida
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  2. Dina Tavares
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  3. Delfim F. M. Torres
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Corresponding author

Correspondence to Delfim F. M. Torres .

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Almeida, R., Tavares, D., Torres, D.F.M. (2019). Fractional Calculus. In: The Variable-Order Fractional Calculus of Variations. SpringerBriefs in Applied Sciences and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-94006-9_1

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  • DOI: https://doi.org/10.1007/978-3-319-94006-9_1

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