Strong convergence rates for the approximation of a stochastic time-fractional Allen–Cahn equation

Mariam Al-Maskari, Samir Karaa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The paper is concerned with the strong approximation of a stochastic time-fractional Allen-Cahn equation driven by an additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time; namely, a Caputo fractional derivative of order α∈(0,1), and a Riemann–Liouville fractional integral operator of order γ∈[0,1] applied to a Gaussian noise. We approximate the model by a standard piecewise linear finite element method (FEM) in space and the classical Grünwald–Letnikov method in time (for both time-fractional operators), and the noise by the L2-projection. Spatially semidiscrete and fully discrete schemes are analyzed and strong convergence rates are obtained by exploiting the temporal Hölder continuity property of the solution. Numerical experiments are presented to illustrate the theoretical results.

Original languageEnglish
Article number107099
JournalCommunications in Nonlinear Science and Numerical Simulation
Publication statusPublished - May 2023


  • Error estimates
  • Finite element method
  • Fractional derivative
  • Stochastic Allen–Cahn equation

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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