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arXiv · 2609.32417

Stochastic maximal $L^p$-regularity for non-autonomous evolution equations with fractional derivative in UMD spaces

Lu Lu Tao·Jia Wei He
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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 $L^p$-regularity results. Our results are applied to non-autonomous stochastic diffusion equation and stochastic fractional reaction-diffusion SIR model.

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Lu Lu Tao, Jia Wei He. 2026-09-26. Stochastic maximal $L^p$-regularity for non-autonomous evolution equations with fractional derivative in UMD spaces. https://arxiv.org/abs/2609.32417

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