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Published in:
Fractional Calculus Read chapter Read first chapter

2019 | OriginalPaper | Chapter

3. Expansion Formulas for Fractional Derivatives

Authors : Ricardo Almeida, Dina Tavares, Delfim F. M. Torres

Published in: The Variable-Order Fractional Calculus of Variations

Publisher: Springer International Publishing

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Abstract

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.

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previous chapter The Calculus of Variations
next chapter The Fractional Calculus of Variations
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Metadata
Title
Expansion Formulas for Fractional Derivatives
Authors
Ricardo Almeida
Dina Tavares
Delfim F. M. Torres
Copyright Year
2019
Book
The Variable-Order Fractional Calculus of Variations

Print ISBN: 978-3-319-94005-2

Electronic ISBN: 978-3-319-94006-9

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-94006-9_3

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