Skip to content
DraconiticResearch
Search Sources API
197,785 studies31 sourcesUpdated 3 min ago
PreprintarXiv licencearXiv

Stochastic maximal Lp-regularity for non-autonomous evolution equations with fractional derivative in UMD spaces

  • Lu Lu Tao
  • Jia Wei He
Open at sourcePDFDOICite

Abstract

This paper is concerned with the maximal regularity theory for non-autonomous stochastic evolution equations with a generalized fractional derivative in UMD spaces. The generalized time-fractional derivative provides a unified framework covering both the classical Riemann-Liouville and Caputo fractional derivatives, which accommodates a wider class of anomalous diffusion processes with intermediate memory effects. Based on the singularities of the initial term and the stochastic convolution kernel, a time-weighted space and a regular-singular decomposition are used to obtain the well-posedness, space-time regularity, and stochastic maximal Lp-regularity results. Our results are applied to non-autonomous stochastic diffusion equation and stochastic fractional reaction-diffusion SIR model.

Related

  1. Weyl Pseudo Almost Periodic Type Solutions to Semilinear Stochastic Evolution Equations Driven by Fractional Brownian Motion
    Dimplekumar N. Chalishajar, Marko Kostic, Daniel Velinov
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsProbabilityarXiv
  2. A Numerical Analysis for Solving the Time-Fractional Cattaneo Model Involving the Riesz Space-Fractional Derivative
    Mousa J. Huntul, Abdullah A. Zaagan
    Fractal and FractionalPeer-reviewedCC BY 4.0Analysis & PDEsCrossref
  3. Stabilization of a degenerate beam on an elastic foundation with axial force under fractional derivative-type delayed boundary feedback
    Lanzhi Cao, Sheng-Jie Li, Shugen Chai
    Electronic Journal of Differential EquationsPeer-reviewedCC BYFull textGeneral mathematicsDOAJ
  4. Sharp Holder regularity for autonomous Beltrami equations
    Jie Huang, Jian-Feng Zhu
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Asymptotic behavior of bounded Mild Solutions to some fractional differential equations involving the ψ-Hilfer derivative
    Adama Kabore, Pihiré Vincent Ouena, Moumini Kéré +1
    HALPreprintCC BY-NC-SA 4.0Full textGeneral mathematicsHAL

Cite

BibTeXRIS
BibTeX
@misc{tao2026stochastic,
  title = {{Stochastic maximal $L^p$-regularity for non-autonomous evolution equations with fractional derivative in UMD spaces}},
  author = {Lu Lu Tao and Jia Wei He},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32417},
  eprint = {2609.32417},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32417},
}
RIS
TY  - UNPB
TI  - Stochastic maximal L^p-regularity for non-autonomous evolution equations with fractional derivative in UMD spaces
AU  - Lu Lu Tao
AU  - Jia Wei He
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32417
UR  - https://arxiv.org/abs/2609.32417
AB  - This paper is concerned with the maximal regularity theory for non-autonomous stochastic evolution equations with a generalized fractional derivative in UMD spaces. The generalized time-fractional derivative provides a unified framework covering both the classical Riemann-Liouville and Caputo fractional derivatives, which accommodates a wider class of anomalous diffusion processes with intermediate memory effects. Based on the singularities of the initial term and the stochastic convolution kernel, a time-weighted space and a regular-singular decomposition are used to obtain the well-posedness, space-time regularity, and stochastic maximal L^p-regularity results. Our results are applied to non-autonomous stochastic diffusion equation and stochastic fractional reaction-diffusion SIR model.
ER  -