Differential operator multiplication method for fractional differential equations

Shaoqiang Tang, Yuping Ying, Yanping Lian, Stephen Lin, Yibo Yang, Gregory J. Wagner, Wing Kam Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Fractional derivatives play a very important role in modeling physical phenomena involving long-range correlation effects. However, they raise challenges of computational cost and memory storage requirements when solved using current well developed numerical methods. In this paper, the differential operator multiplication method is proposed to address the issues by considering a reaction–advection–diffusion equation with a fractional derivative in time. The linear fractional differential equation is transformed into an integer order differential equation by the proposed method, which can fundamentally fix the aforementioned issues for select fractional differential equations. In such a transform, special attention should be paid to the initial conditions for the resulting differential equation of higher integer order. Through numerical experiments, we verify the proposed method for both fractional ordinary differential equations and partial differential equations.

Original languageEnglish (US)
Pages (from-to)879-888
Number of pages10
JournalComputational Mechanics
Volume58
Issue number5
DOIs
StatePublished - Nov 1 2016

Keywords

  • Anomalous diffusion
  • Differential operator multiplication
  • Fourier transform
  • Fractional calculus

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Differential operator multiplication method for fractional differential equations'. Together they form a unique fingerprint.

Cite this