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Numerical Methods for Fractional Differential Equations

In: Fractional Derivative Modeling in Mechanics and Engineering

Author

Listed:
  • Wen Chen

    (Hohai University, College of Mechanics and Materials)

  • HongGuang Sun

    (Hohai University, College of Mechanics and Materials)

  • Xicheng Li

    (University of Jinan, School of Mathematical Sciences)

Abstract

This chapter presents some typical numerical methods for time and space fractional differential equations. Discretization schemes for the Grünwald–Letnikov, Riemann–Liouville, Caputo, fractal and positive time-fractional derivatives are separately discusse, and validated by easy-to-follow numerical examples. Despite being different from “fractional derivative”, fractal derivatives are still included in this chapter. For the convenience of discussions, we call the equations having fractional derivatives with respect to time/space variable the time/space fractional differential equations (TFDEs/SFDEs for short), respectively. If both time and space fractional derivatives are involved, we call the equations time–space fractional differential equations (TSFDEs).

Suggested Citation

  • Wen Chen & HongGuang Sun & Xicheng Li, 2022. "Numerical Methods for Fractional Differential Equations," Springer Books, in: Fractional Derivative Modeling in Mechanics and Engineering, chapter 0, pages 285-333, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-8802-7_6
    DOI: 10.1007/978-981-16-8802-7_6
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