Fractional stochastic heat equation with mixed operator and driven by fractional-type noise
Mounir Zili,
Eya Zougar,
Mohamed Rhaima
Abstract:<p>We investigated a novel stochastic fractional partial differential equation (FPDE) characterized by a mixed operator that integrated the standard Laplacian, the fractional Laplacian, and the gradient operator. The equation was driven by a random noise, which admitted a covariance measure structure with respect to the time variable and behaved as a Wiener process in space. Our analysis included establishing the existence of a solution in the general case and deriving an explicit form for its covariance… Show more
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