Skip to content
DraconiticResearch
Search Sources API
178,970 studies31 sourcesUpdated 52 min ago
Peer-reviewedCC BY 4.0Mathematics

Recovering the Fractional Order and an Initial Value Simultaneously in a Time-Fractional Diffusion-Wave Equation

  • Kun Wang1
  • Jun Xian1,2
  • Lei Zhang2
  1. 1School of Mathematics and Statistics, Qinghai Normal University, Xining 810001, China
  2. 2College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
Open at sourceDOICite

Abstract

For a one-dimensional time-fractional diffusion-wave equation, we investigate joint recovery of its fractional order and the initial velocity from measurements taken at one interior point. Uniqueness is proved through analytic continuation, Laplace transforms, an integral mean value theorem, and Mittag-Leffler function properties. The ill-posed reconstruction is regularized in a Bayesian setting using the iterative regularizing ensemble Kalman method. The posterior measure is shown to exist and to depend stably on the data; its numerical approximation converges under an assumed error bound for the forward solver. The resulting method is assessed in three numerical tests, which illustrate its effectiveness as well as its stability.

Related

  1. Recovering the reaction coefficient in a time-fractional diffusion equation with variable coefficients in any spatial dimension
    D. K. Durdiev
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. Logarithmic stability for recovering initial data of fractional heat equations from thin-set observations
    Kai Yu, Zhiyuan Li
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Stability in recovering the order of a time-fractional evolution equation
    Ravshan Ashurov, Masahiro Yamamoto
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Subdivision-based collocation methods for time fractional convection diffusion reaction equation with environmental and biomedical applications
    Saima Bibi, Syeda Tehmina Ejaz
    Scientific ReportsPeer-reviewedCC BY-NC-ND 4.0Full textGeneral mathematicsCrossref
  5. On the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data
    Yi C. Huang, Ryunosuke Kusaba
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@article{wang2026recovering,
  title = {{Recovering the Fractional Order and an Initial Value Simultaneously in a Time-Fractional Diffusion-Wave Equation}},
  author = {Kun Wang and Jun Xian and Lei Zhang},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14193641},
  url = {https://www.mdpi.com/2227-7390/14/19/3641},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Recovering the Fractional Order and an Initial Value Simultaneously in a Time-Fractional Diffusion-Wave Equation
AU  - Kun Wang
AU  - Jun Xian
AU  - Lei Zhang
PY  - 2026
DA  - 2026/10/08
JO  - Mathematics
DO  - 10.3390/math14193641
UR  - https://www.mdpi.com/2227-7390/14/19/3641
AB  - For a one-dimensional time-fractional diffusion-wave equation, we investigate joint recovery of its fractional order and the initial velocity from measurements taken at one interior point. Uniqueness is proved through analytic continuation, Laplace transforms, an integral mean value theorem, and Mittag-Leffler function properties. The ill-posed reconstruction is regularized in a Bayesian setting using the iterative regularizing ensemble Kalman method. The posterior measure is shown to exist and to depend stably on the data; its numerical approximation converges under an assumed error bound for the forward solver. The resulting method is assessed in three numerical tests, which illustrate its effectiveness as well as its stability.
SN  - 2227-7390
ER  -