Error Estimates for Approximations of Time-Fractional Biharmonic Equation with Nonsmooth Data

Mariam Al-Maskari, Samir Karaa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider a time-fractional biharmonic equation involving a Caputo derivative in time of fractional order α∈ (0 , 1 ) and a locally Lipschitz continuous nonlinearity. Local and global existence of solutions is discussed and detailed regularity results are provided. A finite element method in space combined with a backward Euler convolution quadrature in time is analyzed. Our objective is to allow initial data of low regularity compared to the number of derivatives occurring in the governing equation. Using a semigroup type approach, error estimates of optimal order are derived for solutions with smooth and nonsmooth initial data. Numerical tests are presented to validate the theoretical results.

Original languageEnglish
Article number1
Pages (from-to)8
Number of pages1
JournalJournal of Scientific Computing
Issue number1
Publication statusPublished - Aug 22 2022


  • Biharmonic equation
  • Convolution quadrature
  • Finite element method
  • Nonsmooth initial data
  • Optimal error estimate
  • Semilinear time-fractional equation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Numerical Analysis
  • General Engineering
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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