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<p>We investigate a stochastic fractional partial differential equation (SFPDE) with a mixed operator that combines the standard Laplacian, the fractional Laplacian, and a gradient operator. The equation is driven by Gaussian noise that behaves as a Wiener process in space and a bi-fractional Brownian motion in time. The necessary and sufficient conditions for the existence of the mild solution are explored, along with an analysis of the regularity properties of the solution’s sample paths.</p>

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Stochastic fractional PDEs with mixed operators: existence and path regularity

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Eya Zougar

摘要

We investigate a stochastic fractional partial differential equation (SFPDE) with a mixed operator that combines the standard Laplacian, the fractional Laplacian, and a gradient operator. The equation is driven by Gaussian noise that behaves as a Wiener process in space and a bi-fractional Brownian motion in time. The necessary and sufficient conditions for the existence of the mild solution are explored, along with an analysis of the regularity properties of the solution’s sample paths.