Expansion Formulas for Fractional Derivatives

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


In this chapter, we present a new numerical tool to solve differential equations involving three types of Caputo derivatives of fractional variable-order. For each one of them, an approximation formula is obtained, which is written in terms of standard (integer order) derivatives only. Estimations for the error of the approximations are also provided. Then, we compare the numerical approximation of some test function with its exact fractional derivative. We present an exemplification of how the presented methods can be used to solve partial fractional differential equations of variable-order.


Fractional Derivative Expansion Formula Caputo Derivative Variable Fractional Order Fractional Partial Differential Equations 
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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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